To prepare dough: Whisk whole-wheat flour, all-purpose flour, and 2 teaspoons salt in a large bowl. Whisk 1/3 cup oil and eggs in a small bowl. Add to the dry ingredients along with 1 cup warm water and stir to combine. Add more water, 1 tablespoon at a time, stirring, until a soft, slightly sticky dough forms. Knead a couple of times in the bowl. Shape into 3 disks, wrap each in plastic wrap, and chill for 1 hour.
To prepare filling: Place potatoes in a large saucepan and cover with water. Bring to a boil and cook until very tender, 15 to 17 minutes.
Meanwhile, heat 1 1/2 teaspoons oil in a large skillet over medium heat. Add onion and cook, stirring occasionally, until tender and beginning to brown, about 5 minutes.
When the potatoes are done, drain well and return to the pan. Mash the potatoes with cottage cheese, then stir in the onion, sauerkraut, Cheddar, 1/2 teaspoon salt, and pepper.
To prepare pierogi: Put a large pot of water on to boil. Coat 1 large baking sheet with cooking spray; place next to the stove. Very generously dust 2 more large baking sheets with flour.
Place a small bowl of water and the pierogi filling near your work area. Roll out one disk of dough on a well-floured surface until it's about 1/16 inch thick (an approximate 16- by 20-inch oval). Using a 3 1/2-inch round cutter, cut out dough. Cover the dough scraps with a clean kitchen towel. Moisten the edges of each round with water. Place a level tablespoon of the filling in the center of each round. Fold the dough over the filling and press the edges (the pierogi will be very full); crimp with a fork to seal completely. Place on a floured baking sheet. Repeat this process with the two remaining disks of dough. Then repeat with the dough scraps, rerolling them as needed to make enough pierogi to use up all the filling (48-50 total). Discard any remaining dough.
Cook the pierogi in 5 batches in the boiling water until they float to the top. Transfer with a slotted spoon to the baking sheet coated with cooking spray, letting water drain off from the spoon before transferring them.
Preheat oven to 200 degrees F.
Heat 1 tablespoon each oil and water in a large nonstick skillet over medium heat. Add 8 to 10 pierogi and cook until browned on both sides, 6 to 10 minutes total. Transfer to a baking sheet and keep warm in the oven while you prepare the rest. Add 8 to 10 more pierogi to the pan, drizzle in 1 tablespoon each oil and water and shake the pan to loosen the pierogi. Cook until browned on both sides; reduce the heat as necessary to prevent overbrowning. Repeat with the remaining pierogi, oil and water.
Serve sprinkled with parsley, if desired.
Exchanges: 2 1/2 starch, 2 1/2 fat Carbohydrate Servings: 2 1/2 Nutrition Bonus: Folate (18% daily value).
