In a large bowl, stir together the ground meat, parboiled rice, sautéed onion, breadcrumbs, beef broth, and parsley. Add salt and pepper and up to 1 tablespoon of sugar, if desired. The mixture should be very moist.
Place a steamed cabbage leaf on a cutting board. Trim a little bit of the core off of the leaf to make it easier to roll. Place a heaping 2 tablespoons of the meat mixture at the core end of the cabbage leaf (use less filling for particularly small leaves).
Start to roll, fold in each side, and then continue rolling to seal. Don’t roll the cabbage rolls too tightly. The rice expands as it cooks, so cabbage rolls stuffed too tightly might tear or burst in the cooking process, causing that yummy filling to spill out and fall apart. You can use toothpicks to secure the rolls if you like, but it’s not necessary. Repeat with the remaining cabbage leaves and filling.
Place the stuffed cabbage rolls seam-side down in the Dutch oven that has bacon grease in the bottom. Stack the rolls, as necessary, and season with salt and pepper. Spread the condensed soup (not diluted) over top.