Mix together the warm water, granulated sugar, and the active dry yeast. Stir to dissolve the sugar and set aside to let it foam up.
Combine in a large bowl, the flour and the salt. Stir to combine.
Add to the dry ingredients, the sour cream, eggs, oil, and yeast mixture. Mix the dough with a spoon until all the dry ingredients have been absorbed.
Transfer the dough to a lightly floured surface and knead it by folding it onto itself about 5-6 times, or until the dough is smooth. Shape into a ball and place back into the bowl. Cover with plastic and let it rest for 30 minutes.
Assemble the Pyrizhky
Make the filling by cooking the chopped bacon and the onions over medium heat. Take the cooked bacon and onion mixture off the heat.
Rince the sauerkraut and squeeze out any excess liquid from it. Chop it finely and then add to the pan with the cooked bacon and onions.
Divide the dough into 20 equal pieces. Use a food scale to weigh the total weight of the dough and divide it by 20.
Preheat the oven to 350F and line a baking tray with parchment paper.
Use your finger to flatten out each piece of dough into a 3 ½ inch disk. Hold the disk in one hand and use a spoon to place 2-3 tablespoon of the cabbage filling in the centre of the disk.
Close up the bun by bring the dough over the filling like a string purse and sealing it shut by pinching it closed with your fingers. Form in a kind of oblong.
Place the shaped Pyrizhky, seam down, on a parchment paper lined baking tray. Cover with a plastic wrap and proof for 1 hour, or until doubled.
Make the egg wash by mixing together the yolk and the milk. Brush each Pyrizhky with the egg wash. Bake in the preheated oven for 20-25 minutes or lightly golden.
Remove from the oven and brush with the melted butter right away. Let them cool 10-15 minutes before serving.