1. Heat a medium-size saucepan of water to a boil over medium-high heat. Trim the root ends from the onions, leaving the core intact. Drop the onions into the boiling water. Bring back to a boil and cook the onions 2 minutes. Drain and run under cold water until they are cool enough to handle. Slip the skins off the onions, leaving the onions whole.
2. Remove any wilted or damaged leaves from the greens. Pull the leaves from the stems. Trim the stems and cut them crosswise into 1-inch pieces. Cut the leaves crosswise into 2-inch pieces. Wash and dry the stems and leaves separately and set aside. (If making the stew in advance, store the leaves in Zipper-top bags in the refrigerator box up to 2 days.)
3. Rub the short ribs generously with salt and pepper. Heat the oil in a heavy large pot or Dutch oven over medium-high heat. Add the short ribs and cook, turning as necessary, until they are well browned on all sides, about 10 minutes. If the bits that stick to the pot start to burn, reduce the heat to medium. Remove the short ribs.
4. Add the button mushrooms, portobello wedges, onions, and stems from the greens to the pot. Pour in the stock, wine, and tomatoes. Tuck the ribs into the mixture. Heat the liquid to a boil, reduce the heat, and simmer, uncovered, until the beef is tender, about 2½ hours. About halfway through, add salt and pepper to taste, keeping in mind the liquid will be further reduced and the seasoning will be intensified. (The short ribs may be prepared to this point up to 2 days in advance. Cool completely, then refrigerate until needed. Bring the stew to a simmer and simmer 10 minutes before continuing.)
5. Remove the short ribs from the pot. Heat the liquid to a boil over medium-high heat. Stir in the leaves from the greens and boil until tender, about 8 minutes. Check the seasoning, adding salt and pepper if necessary. Divide the contents of the pot among 4 shallow serving bowls and top each with 2 short rib pieces.