Brown the Beef: Heat a large Dutch oven or stockpot over medium-high heat. Add the olive oil, ground beef, ¼ teaspoon of the salt, and cook for 5-6 minutes, breaking it into small crumbles, until well browned and no pink remains. Drain any excess fat.
Cook the Vegetables: Add the onion and carrots to the same pot and cook for 3-4 minutes until softened.
Add the garlic, paprika, oregano, pepper, and ¼ teaspoon of salt, and cook for 1 minute until fragrant, stirring constantly.
Add the Liquids: Stir in the Worcestershire sauce, apple cider vinegar, and brown sugar, stirring to coat the meat and vegetables.
Add the fire-roasted tomatoes, tomato sauce, beef broth, and ½ teaspoon of salt, and stir to combine, scraping up any browned bits from the bottom of the pot.
Simmer: Add the cabbage, rice, and bay leaf, stirring until well incorporated. Bring to a boil over medium-high heat, then reduce the heat to low.
Cover and simmer for 25-30 minutes, stirring occasionally, until the rice is tender and the cabbage is soft and silky.
Remove the bay leaf. Taste for seasoning and adjust with salt, pepper, or a splash more apple cider vinegar as needed.
Serve: Ladle into bowls and top with fresh parsley.