In a large skillet, saute chopped onion with 2 Tbsp oil, until onions are tender. Add the shredded carrots and saute until tender.
Then add the mushrooms with 1 Tbsp oil, and saute until the mushrooms are cooked and browned.
Add the shredded cabbage. garlic, and water into the skillet. Turn heat down to medium/low and braise 10 minutes. Season with salt and pepper to taste and add fresh herbs. Remove from heat to cool.
Generously flour working area and transfer the dough onto surface. Divide the dough into 20 equal parts. (see note)
Roll out each of the parts into about a 3½" round circle. Divide the cabbage filling among the 20 pieces and place into the center of dough.Fold the dough in half and seal the edges by pinching dough together. Repeat with all of the piroshki. Press down on the pies so it's flat and even in size.
In a large pot, cover the bottom with oil about 2 inches deep and heat oil to 330°F.
Add the piroshki into the pot, careful not to overcrowd the pot. Fry 2-3 minutes per side, until golden. Remove onto a plate lined with paper towel. Repeat with all the piroshki.
Serve with sour cream.
Divide dough: Cut dough into four equal parts, then gently shape each part into a log. Cut each part into five pieces, equaling 20 pieces.