Boil the potatoes in plenty of water until soft. Drain, and set aside to cool.
When they are cool enough to comfortably handle, peel the potatoes with a sharp paring knife, and “rice” them in a ricer or the grating attachment of a food processor. (You should have about 3 cups cooked, riced potatoes.) Transfer to a medium-sized bowl.
Add 1½ cups flour and 1 teaspoon salt to the potatoes. Mix first with a spoon and then with your hand to make a dough. Add the milk a little at a time as needed, so the dough becomes soft and workable. You want it pliable but not sticky.
Put up a large pot of salted water to boil.
Meanwhile, lightly flour a clean, dry surface. Turn out the dough and push it together with your hands, but don’t otherwise knead. Divide the dough in two, and roll each piece until it is about ½ inch thick. Use a plain dinner knife to cut 1-inch squares (or diamonds, or triangles, or rhomboids, or whatever).
When the water boils, turn it down to a simmer, and add as many pieces of dough as will fit without crowding. They will soon rise to the surface of the simmering water. Cook them for 3 minutes, then scoop them out with a strainer or a slotted spoon and put them on a plate. Continue with another batch until all the dumplings are poached. At this point, they can be stored in an airtight container in the refrigerator for up to 3 days.
Heat a large nonstick skillet and add about a tablespoon of butter. When it is melted, add as many dumplings as will comfortably fit in a single layer and sprinkle lightly with salt. Lower the heat to medium, and sauté the dumplings on one side for 8 to 10 minutes, or until golden brown.
Sprinkle with the sage and chives, and turn the dumplings over. Sauté another 8 to 10 minutes, then transfer to a plate lined with paper towels. Serve as soon as possible.