In a larger bowl, combine all filling ingredients and mix thoroughly with your hands until integrated. Set aside.
In a big bowl add lukewarm water. Separate sour cabbage leaves from the cabbage head one by one. Stop when you have about ¼ to ⅓ of the cabbage head left. (Keep the remaining cabbage head(s).) Dip each leaf into the bowl with water, quickly take it out, and set it aside on a plate. (This is to wash the extra saltiness off.) You can try a piece to see whether it's still too salty to your taste. If it is, you can dip it in the water again.
Place cabbage leaves on a cutting board (one by one), and cut out the thick middle vein from each leaf. (Set veins aside with the remaining cabbage head.) Proceed to cut each leaf in half. If the leaves are large, cut them into three, even four pieces.
Take one leaf piece into your palm. Place about one tablespoon of the filling in the middle toward the edge of the leaf. Fold the longer leaf end on one side of the filling toward the filling, and roll everything away from you, squeezing lightly as you roll. Once rolled, tuck the other side of the leaf in with your finger. (You'll essentially end up with a tiny burrito-like roll.) Set your sour cabbage roll aside.
Repeat until you run out of ingredients. (You should have about 25-35 rolls with this amount of ingredients, depending on how large you make your rolls. The best rolls are about 1.5x2.5 inches.)
Combine leaf veins with the remaining cabbage head and dice them.
In a large pot, heat oil on medium. When it heats up, whisk in the flour until you get a roux (2-3 minutes). Add in the tomato sauce and 1 cup of hot water. (If using tomato paste, add 1.5 cups of hot more.)
Place the first layer of rolls on the bottom of the pot. Follow up with a handful of meat, and diced cabbage. Repeat layering until you run out of ingredients. Cover with water (or broth) at the evel about the thickness (an inch) of a finger above the rolls.
Cook on low for 3 hours. Do not stir. Keep replenishing the stew levels so they're at the same level throughout cooking. You'll add about 5 cups of water in total, although this is just an approximation.
Serve anywhere from 2-6 rolls per person, and cover with 1-2 ladles of stew. The best sides are the bread and mashed potatoes. (Optional) Add a dollop of sour cream. Store in the fridge for up to 3 days. Reheating and freezing directions are in the notes.