For the sauce: In a large pot, saute the onion in olive oil until translucent, about three minutes. Add the minced garlic, tomato paste, brown sugar, and balsamic vinegar. Cook for about 30 seconds until fragrant.
Mix in the crushed tomatoes and oregano, season with salt and pepper, reduce heat to medium-low, and simmer sauce for 20 minutes
Bring water to a boil in a large pot and blanch the cabbage for about a minute. Remove the leaves when tender and flexible.
Preheat the oven to 350F. Make the filling: In a medium-sized bowl, mix the ground beef, one cup of sauce, rice, bread crumbs, chopped onion, and parsley. Season with salt and pepper
Make the rolls: remove the tough part of the white vein in the middle of the leaves and add ⅓ cup of filling on one end
Roll up, tucking in the sides as you go. Keep your rolls seam-side down as you finish rolling all of them
Spread one cup of sauce on the bottom of a 9 x 13-inch casserole dish and arrange the rolls seam-side down on top of the sauce
Spoon the rest of the sauce on top of the rolls, cover with aluminum foil and bake for 1 hour and 15 minutes.