Cook the potatoes and whole onion in boiling water to cover for 20 minutes or until tender. Drain; discard onion. Mash the potatoes. Add the chopped onion and the next 3 ingredients, stir well.
Combine the flour, egg yolks, 1/2 teaspoon salt, 3/4 cup boiling water, and 1 tablespoon vegetable oil. Stir well. Turn the dough out onto a floured surface, and knead lightly 4 or 5 times. Cover; let rest for 30 minutes.
Roll the dough out to 1/8 inch thickness on a floured surface; cut with a 3 inch cutter. Divide the potato mixture evenly among circles. Moisten the edges of the dough with water. Fold the circles in half; press the edges together with a fork to seal.
Combine 1 tablespoon oil, 1 tablespoon salt, and 4 quarts of water in a Dutch oven; bring to a boil. Drop the pierogi, a few at a time, into the boiling water; cook for 5 minutes or until the pierogi rise to the surface. Remove with a slotted spoon. Brush with melted butter; serve with sour cream.