Bring a large pot of salted water to a boil. Carefully remove the core from the cabbage head using a sharp knife, then submerge the whole cabbage in the boiling water for 5 to 8 minutes until the outer leaves soften and peel away easily.

Gently peel off 12 large leaves from the cabbage, placing them on paper towels to drain. Use a paring knife to shave down the thick center vein on the back of each leaf so they roll up easily without breaking.

In a large bowl, combine the ground beef, cooked white rice, chopped onion, minced garlic, egg, dried oregano, salt, and black pepper. Mix thoroughly with your hands until the ingredients are fully incorporated and hold together well.

Lay a cabbage leaf flat on a clean surface with the stem end facing you. Place about 3 tablespoons of the beef mixture in the center, fold the bottom up, tuck in the sides, and roll tightly toward the top.

In a medium bowl, whisk together the tomato sauce, crushed tomatoes, brown sugar, and lemon juice to create a sweet and tangy braising liquid. Spread a thin layer of this sauce across the bottom of a large Dutch oven.

Arrange the cabbage rolls seam-side down in the Dutch oven, fitting them snugly together in a single or double layer. Pour the remaining tomato sauce evenly over the top, ensuring all the rolls are well coated.

Place the Dutch oven over medium heat and bring the liquid to a gentle simmer. Cover tightly with a lid, reduce the heat to low, and cook for 60 minutes until the cabbage is tender and the meat filling is fully cooked through.

Let the dish rest for 5 minutes before serving to allow the sauce to settle. Plate the rolls warm, spooning the rich tomato sauce generously over the top, and garnish with fresh dill and a dollop of sour cream if desired.