1. Trimming the ribs: trim any excess fat from the short ribs, but don’t take off any of the silver skin or tough-looking bits that hold the ribs together.
2. Salting the ribs – 1 or 2 days before braising (optional): arrange the short ribs in a loose layer on a tray or on a nonreactive dish. Sprinkle them all over with 1 ½ to 2 teaspoons salt (there’s no need to rub the salt into the meat) and cover loosely with waxed paper or plastic wrap. Refrigerate for 1 to 2 days.
3. Heat the oven to 300 degrees: pat the ribs dry with a paper towel, but don’t try to rub off the salt. Season with pepper. (If you didn’t salt the ribs in advance, season them with both salt and pepper.)
4. Browning the ribs: pour the oil into a Dutch oven or other heavy braising pot (4- to 6-quart) wide enough to accommodate the short ribs in a crowded single layer and heat over medium heat. Add only as many ribs as will fit without touching, and brown them, turning with tongs, until chestnut-brown on all sides, about 4 minutes per side. Transfer the seared ribs to a platter, without stacking, and continue until all the ribs are browned. (Alternatively, you may want to brown the ribs under the broiler to avoid some of the spatter, although this will mean dirtying another pan.)
5. The aromatics: Pour off and discarded all but about a tablespoon for fat from the pot. If you there are any charred bits in the pot, wipe them out with a damp paper towel, being careful not to remove the precious caramelized drippings. Return the pot to medium-high heat and add the onions and carrot. Season with salt and pepper and sauté, stirring a few times, until the vegetables start to brown and soften, about 5 minutes.
6. The braising liquid: add the ale and bring to a full boil. Boil for 2 minutes, scraping the bottom of the pot with a wooden spoon to dislodge and dissolve any tasty bits cooked onto it. Pour in the stock, bring again to a boil, and reduce the heat to a simmer. Return the ribs to the pot, along with any juices released as they sat. Tuck the rosemary sprig and bay leaves in between the ribs. The ribs should be partially submerged in the liquid. If necessary, add a bit more ale or water.
7. The braise: cover with a sheet of parchment paper, pressing down so that it nearly touches the ribs and hangs over the edges of the pot by about an inch. Set the lid securely in place. Slide the pot into the oven and braise at a gentle simmer, turning the ribs with tongs so as not to tear up the meat, every 40 to 45 minutes, until fork-tender, about 2 ½ hours. Check under the lid after the first 10 minutes to see that the liquid isn’t simmering too aggressively; if it is, lower the oven temperature 10 or 15 degrees.
8. Meanwhile, prepare the glaze: while the ribs are braising, combine the maple syrup with the rosemary sprigs in a small saucepan. Heat to a gentle boil over medium heat. Turn off the heat, cover, and set aside to infuse for 1 hour. (The glaze can be made up to a few days ahead and refrigerated.)
9. Removing the ribs from the braising liquid: when the ribs are tender and the meat is pulling away from the bones, use tongs or a slotted spoon to carefully transfer them to a flameproof gratin dish or shallow baking dish that is large enough to accommodate them in a single layer. Try your best to keep the ribs on the bones and intact, but don’t worry if some bones slip out. (Discard these clean bones, or save them for the dog.) Scoop out the vegetables with a slotted spoon and arrange them around the ribs. Cover loosely with foil to keep warm.
10. Finishing the braising liquid: tilt the braising pot to collect the juices in one end and skim off as much surface fat as you can with a large spoon. If there is more fat than you care to skim off a spoonful at a time, transfer the braising liquid to a gravy separator and then pour the liquid into a medium saucepan leaving the fat behind. If the braising liquid exceeds ½ cup, bring it to a vigorous simmer over medium-high heat and cook it down to close to ½ cup, 10 to 15 minutes; it should have a syrupy consistency. Taste and season with salt and pepper. Keep warm.
11. Glazing the short ribs: heat the broiler on high. If the glaze has been refrigerated, warm it slightly so that it’s pourable. Remove the rosemary sprigs, lightly running your fingers down the length of the sprigs so you save every drop of glaze. Put the horseradish in a small strainer (a tea strainer works great) or in the palm of your hand and squeeze over the sink to eliminate as much liquid as possible, then stir the horseradish into the glaze. Brush the glaze on the tops of the short ribs. Pour the reduced braising liquid around the ribs – don’t pour it over the ribs, or you’ll wash off the glaze. Slide the ribs under the broiler and broil until the surface of the ribs develops a shiny, almost caramelized glaze and you can hear them sizzle, about 4 minutes.
12. Serving: Transfer the ribs to serving plates – the number per serving depends on the size of the ribs. Spoon the braising liquid around, not over, the ribs, and serve immediately.
Browning the short ribs under a broiler:
You can also sear the ribs under the broiler, not in the braising pan on top of the stove. In place of step 4, preheat the broiler on high and adjust the oven rack so that it sits about 6 inches from the flames or heating element. Arrange the ribs 1 to 2 inches apart on a rimmed baking sheet (a half sheet pan) or broiler pan, and slide them under the broiler. Broil, turning with tongs as each side browns, until sizzling and chestnut brown on all sides, about 5 minutes per side. Transfer the ribs to a platter, without stacking, pour off and discard the grease remaining in the pan, and deglaze to capture any precious caramelized beef drippings: set the pan over medium-high heat, add a small amount of ale, stock, or water, and bring to a boil, stirring with a wooden spoon to scrape up and dissolve the drippings. Reserve this liquid.
Heat 1 tablespoon oil (you will only need 1 tablespoon in all if using this method) in a medium Dutch oven or other heavy braising pot (4-quart) over medium-high heat. Add the onion and carrot to the pot and continue with Step 5 as directed above. In step 6, add the deglazing liquid from the broiler pan, along with any meat juices, when you add the short ribs.