Combine flour and salt in a large bowl, forming a well in the middle. Add butter and milk and mix lightly until flour is absorbed. (Add a little warm water as needed).
Knead until dough sticks together, cover, and allow to rest for a few minutes, then knead until smooth. Cover and set aside. (The dough should be somewhat soft since more flour is added as dough is rolled out.)
Or, in the processor, combine flour, salt, and butter and stir a few times. With the machine running, add liquids until ball forms. Allow to rest a few minutes, then process until smooth.
Place dough in a lightly oiled bowl, turn and cover for about 30 minutes before rolling out. (It may be wrapped in plastic and refrigerated for a day or so, brought to room temperature, and then rolled out.)
Place a fourth of the dough on a floured work surface; cover the remaining dough. Roll into a circle, away from the center, turn over, flour lightly, and roll again to about ¼ inch thickness. Run a hand under the bottom to loosen it. With a 3-inch biscuit cutter or wineglass, cut rounds. Place a tablespoon of filling on one side of each round, flip over the other half, and press the edges together, sealing in the filling. Place dumplings on a floured tray; keep dumplings covered with a towel.
Gently drop 10 – 15 pierogies in 3 quarts of boiling water in a large wide pot or dutch oven. Do not crowd. Stir and cook for 3 to 4 minutes. Drain in a colander. Place on a lightly oiled tray and shake to coat with a thin film of oil (to prevent sticking). Do not pile dumplings on top of each other, as this distorts their shape.
If pierogi are to be frozen, remove them with a slotted spoon when they float to the top. Do not overcook. To freeze, place in the freezer on an oiled cookie sheet while tepid. When they are rigid, store them in tightly sealed plastic bags.
To serve, pierogi may be poached, pan-fried, or steamed, served as an accompaniment to meats, or served with sour cream, chopped sauteed onions, or fried bacon with a little bacon fat.
Potato-Cheese Filling
Peel and quarter potatoes, cover with water, and cook until soft. Meanwhile, cook chopped onions in melted butter until golden. Drain and rice potatoes. Shred cheddar cheese or crumble bryndzia. Add onions, cheese, salt, and pepper to potatoes and mix well. Allow to cool, stirring occasionally. Filling may be refrigerated for several days. Do not freeze filling.
Note: leftovers may be used to make breakfast cake or as filling for potato boats or stuffed peppers.