Prepare pierogi dough of choice and let rest for 30 minutes.
Peel, core, and dice apples into small pieces.
Cook diced apples in a non-stick skillet over medium-low heat for about 10 minutes, stirring often.
Season apples with cinnamon, sugar, and a dash of lemon juice if needed. Adjust to taste.
Divide dough into 2-3 parts. Roll one part thin on a floured surface, but not so thin that it tears. Wrap remaining dough to prevent drying.
Cut palm-sized circles in the rolled dough. Reuse the leftover dough by forming a ball and rolling again.
Place a spoonful of apple filling on each dough circle, fold over, and seal edges, removing as much air as possible. Moisten edges for a better seal. Place formed pierogi on a floured sheet, covered with a damp kitchen towel. Use flour to prevent sticking if they touch. Repeat until all dough or filling is used.
Boil a large pot of salted water (1 tsp salt per quart).
Add pierogi to boiling water, stirring to prevent sticking. Simmer gently for 3-4 minutes after they float to the surface.
Remove with a slotted spoon and serve.