Brown the beef: Heat the olive oil in a large pot or Dutch oven over medium-high heat. Add the ground beef and cook for 5-6 minutes, breaking it into small pieces, until no pink remains and it reaches an internal temperature of 160°F. Pour off any fat beyond about a tablespoon.

Soften the vegetables: Add the onion, carrots, and celery and cook for 5 minutes, stirring, until the onion turns translucent and the celery softens at the edges. Stir in the garlic and cook 30 seconds more, just until it smells sweet.

Wilt the cabbage: Add the chopped cabbage and cook for 3-4 minutes, tossing it through the beef and vegetables, until it collapses enough to fit comfortably in the pot.

Build the broth: Pour in the diced tomatoes with their juice, the tomato sauce, and the beef broth. Add the brown sugar, Italian seasoning, bay leaves, salt, and pepper, and scrape the bottom of the pot to lift the browned bits. Bring it to a boil.

Simmer: Cover, drop the heat to low, and simmer for 20-25 minutes, until the cabbage is tender with a little bite left and the carrots slide off a fork. Stir once or twice along the way.

Finish and taste: Fish out the bay leaves, stir in the parsley, and taste for salt. Canned tomatoes and broth vary a lot in saltiness, so this last taste matters more than the measured teaspoon does.