Heat 2 tablespoons oil in a pot over medium heat, add chopped onions and saute until tender, about 5 minutes. Increase heat to medium-high, add ground beef and saute until no longer pink.
Add 2 teaspoons turmeric powder, crushed tomatoes, chopped bell peppers, water, bay leaf, salt and pepper. Cover the pot and simmer over medium-low heat until all of the liquid is evaporated. Stir occasionally. Add dried barberries (Zereshk) and ground walnuts; cook for 5 more minutes. At the end, discard the bay leaf.
Meanwhile, place the grated potatoes, 1/2 teaspoon turmeric powder, salt and pepper in a large bowl. Slowly add the milk and mix until smooth. If it is too thick, add more milk and if it's too smooth, add less than 2 cups milk. Taste and add more salt and pepper if needed.
Spoon the ground beef mixture into 8x11 inch casserole dish. Sprinkle with oregano.
Spread the potato mixture on top of the beef mixture. Pour 4 tablespoons oil evenly on top.
Place on the middle rack of the oven and broil on low heat until golden brown. Remove from oven and let stand for 5-10 minutes before serving.