Bring a pot of water to a boil and generously salt it. Add the potatoes and boil until very tender. Drain as much of the water from the pan as you can, keeping the potatoes in it. There should be no pooled water in the pan. Add the sticks of butter and caramelized onions, mash until the potatoes are smooth and the butter has melted and incorporated completely. Taste the potatoes and adjust with salt if necessary. Eat as is or use as stuffing in Vareniki.

Combine the flour, water, eggs, butter and salt in the bowl of a stand mixer fitted with a dough hook or a large mixing bowl. Mix vigorously until a shaggy dough forms. If there are big pockets of dry ingredients at the bottom of the bowl, you may need to add water, 1 tablespoon at a time, until you have a cohesive dough. Turn the dough out onto a lightly floured counter and knead until the dough is silky and smooth. Place in a bowl, cover with plastic wrap or a tea towel, and let rest at room temperature for 30 minutes to allow the dough to relax and fully hydrate.

Divide the dough in half and keep the half you’re not working with covered with a towel or plastic wrap. On a lightly floured counter top, roll one half of the dough out to an even 1/16 to 1/8 of an inch thickness. Use a 3 or 3 ½ inch round cutter to cut circles of dough. Reserve the dough scraps to re-roll and cut more circles from when you’re finished. Scoop about 2 teaspoons of the mashed potatoes into the center of each round. Lift and pinch two opposite sites to seal them around the potato filling. Use your fingers to crimp the rest of the half-moon closed. If desired, bring the corners from the straight edge of the half-moon together at the bottom of the dumpling, making it look like a large tortellini. Lay the finished dumplings on a clean platter in a single layer. Repeat with the remaining dough and mashed potatoes until you’ve exhausted one or both of them.

Bring a large pot of water to a vigorous boil and salt it generously. Carefully lower several of the Vareniki into the pot, taking care not to overcrowd the pot. Gently stir to keep them from settling and sticking to the bottom of the pot. Boil the vareniki until they float, then use a slotted spoon to remove, drain, and transfer them to a plate. You can either serve them as is or take them to the next level by melting 4 tablespoons of butter in a stainless steel or cast-iron frying pan over medium heat.

Add the boiled vareniki to the melted butter in a single layer. It will probably fizzle and pop, but should slow down relatively quickly. Let the vareniki fry in the butter, undisturbed, until they release easily from the pan and are golden brown on the underside. Serve hot, topped with sour cream and chopped chives or green onions.