In a large bowl, stir the flour and sea salt together, and push aside to form a well in the bowl. Or, use a stand mixer with dough hook
Add eggs in the center, then the butter and milk, and start mixing dough with fork or dough hook in mixer
Gradually add the potato water, and mix until dough starts to form. Add enough water to form a ball, and knead until no longer sticky. You may not need to use all the water. Add more water if too dry or more flour if dough is still too sticky
Wrap dough ball in plastic wrap, and refrigerate for 20 minutes to rest
Divide dough into 4 separate pieces, and keep covered to prevent drying out
Roll out one piece at a time on a floured surface about ⅙ inch thick, and cut out circular shapes with a drinking glass or round cookie/biscuit cutter about 3 inches in diameter
Place a tablespoon full of filling in center of dough, fold ends over, and pinch together. Dip fingers in a bowl of water to help seal edges
Place pierogi on lightly greased cookie sheet until dough is used up, and keep covered until ready to cook
Bring a large pot of salted water to a gentle boil, and cook pierogi, a few at a time, stirring once or twice so they don't stick, until they float to surface
Remove with slotted spoon, and serve. Or, sauté chopped onion in butter over medium heat until golden brown. Then, fry pierogi with butter and onions until golden brown and onions are caramelized before serving. Add more butter as needed.