Cook potato in boiling water in a medium saucepan 10 minutes or until tender. Drain potato in a colander over a bowl, reserving 2 tablespoons cooking liquid. Return potato to pan. Add reserved cooking liquid; beat at medium speed of mixer until smooth. Set aside.
Melt 1 teaspoon butter in pan over medium heat. Add chopped onion; sauté 5 minutes or until tender. Remove from heat; stir in potato, cheese, and next 4 ingredients (cheese through white pepper). Cover and set aside.
Lightly spoon 2 cups flour into a dry measuring cup; level with a knife. Combine with 1/2 teaspoon salt in a large bowl; make a well in center of mixture. Stir in 1/3 cup water and eggs. Turn dough out onto a lightly floured surface, kneading lightly 4 to 5 times. (Dough may appear dry but will moisten while kneading.) Cover and let rest 10 minutes.
Divide dough into 5 equal portions. Working with 1 portion at a time (cover remaining dough to keep from drying), roll each portion to a 1/8-inch thickness on a lightly floured surface. Cut 5 circles with a 3-inch round cutter,discarding dough scraps. Spoon 2 level teaspoons potato mixture onto half of each circle. Moisten edges of dough with water. Fold dough over filling; press edges together with floured hands to seal. Place pierogi on a large baking sheet sprinkled with 1/3 cup flour. Cover. Repeat procedure with remaining dough and potato filling.
Bring 2 quarts water to a boil in a Dutch oven; add 5 pierogi. Cook 3 minutes or until pierogi float to surface. Remove pierogi with a slotted spoon; place on a wire rack coated with cooking spray. Repeat procedure with remaining pierogi.
Melt 1 1/2 tablespoons butter in a large nonstick skillet over medium heat. Add 1/2 cup sliced onion and 1/4 cup fennel; sauté 10 minutes or until tender. Add 12 pierogi; sauté 5 minutes or until thoroughly heated and lightly browned. Set aside. Repeat procedure with remaining butter, onions, fennel, and pierogi. Serve immediately.