1. To make the caramelized onions, in a medium skillet melt 3 Tbs. of butter over medium-low heat. Add the sliced onions and 1/8 tsp. salt. Cook until onions are brown and soft, about 1 hour, stirring occasionally. Remove from heat and refrigerate for up to 48 hours.
2. For the dough, place the flour in a large bowl. Make a well in the center. Add the water, egg, oil, and salt into the well. Slowly stir the flour into the liquid, mixing until the dough forms a ball, adding a bit more water if necessary. (The dough should be soft.) Let dough rest, covered, for 1 hour.
3. For the filling, bring a large pot of salted water to a boil. Add the potato and boil until tender, about 20 minutes. Meanwhile, in a small skillet melt 2 tsp. unsalted butter over medium-low heat. Add the chopped onions and cook until tender, about 5 minutes. Drain the potatoes and transfer to a medium bowl. Mash with a potato masher. Add the chopped onions, farmer's cheese, colby cheese, and 1/2 tsp. salt. Stir to combine.
4. To assemble the pierogi, lightly flour a clean work surface. Roll the dough into a circle about 1/8-inch thick. Cut out twenty-seven 3 1/2-inch circles with a cookie cutter or wide-mouthed glass, re-rolling scraps as needed. Place 1 Tbs. of filling on the lower half of each circle. Fold dough over in half. Pinch edges, and set aside loosely covered with a kitchen towel.
5. Bring a large pot of salted water to a boil. Add pierogi a few at a time, stirring with a wooden spoon to prevent sticking. Simmer pierogi until they float to the top, about 3 minutes. Remove with a slotted spoon and place in a parchment lined pan or storage container. Repeat with remaining pierogi, separating layers with parchment paper. The cooked pierogi can be refrigerated for up to 3 days or frozen for 3 months. (If frozen, thaw before continuing to step 6.)
6. When ready to serve, in a very large skillet melt 1 Tbs. butter over medium high heat. Add 9 pierogi in a single layer. Cook until each dumpling has a deep brown crust on both sides, about 6 to 8 minutes total. Transfer to a serving dish and repeat with remaining pierogi and butter. Serve with warmed caramelized onions, chives, and sour cream. Season with salt, to taste.