Combine milk and water. Heat in microwave for 45 sec, or on the top stove until barely warm. Add sugar and dry yeast. Mix until sugar dissolves and set it a warm environment to proof, for 15 minutes.
Add eggs, salt, sour cream and mix everything together with the dough hook attachment (or hand whisker) on medium speed. Add melted butter and mix again.
Add 1 cup of flour, mix on low, and then ½ cup at a time after that until all flour is incorporated.
The dough should be thin (starchy) and sticky, unlike for pirozhki baked in the oven.
Cover the dough in the mixer bowl with a clean kitchen towel and let it rise for an hour.
Filling Instructions:
While the dough is rising, make the meat filling (or filling of your choice). Rinse and grind meat. Add egg, shredded garlic, onion, salt, and pepper to taste. Mix everything together with a hand mixer on low until combined. Cover and refrigerate until ready for use.
Assembly Instructions:
The dough should triple in size. Scrape the sides of the mixer with a silicone spatula to deflate the bubbles. Dip your finger in oil and pinch off chunks about ½ cup in size. Flatten each chunk of dough with your hands, place some filling on each dough pancake, bring the surround edges together and pinch to seal in the filling.
Pinch the edges together tightly so they don't come apart at the seams, especially when deep frying. Dip your hands in oil again if necessary and shape the Belyashi into an oval shape.
Frying Instructions:
Pour half a small saucepan of oil. Heat the oil to 300F. Place as many Belyashi as will fit on the surface without overlay. Fry Belyashi for about 2 min on each side or until golden brown.
Place fried Belyashi onto a paper towel to soak in excess oil. Repeat the same steps with the rest of the dough and filling. Form a few Belyashis at a time, while others are frying. Do not make all Belyashi at once then fry them, because they will rise too much by the time they make it in the oil, and will be very airy inside once fried. Not pretty! :)