Heat 1 Tbsp olive oil in a large cast-iron pot over medium-high heat.
Add beef, season with salt and pepper and cook, stirring and breaking up beef occasionally, until browned.
Transfer beef to a plate lined with paper towels while reserving 2 Tbsp of the rendered fat in the pan (or drain off all fat and use 2 more tbsp olive oil), set beef aside.
Add onion and carrots to pan and saute 1 minute, then add cabbage and saute 2 minutes, then add garlic and saute 1 minute longer. Pour in beef broth, tomato sauce, tomatoes, brown sugar, Worcestershire, paprika, oregano, thyme, and bay leaves. Return beef to soup mixture.
Season soup with salt and pepper to taste and bring to a light boil, then add rice, cover pot, and reduce heat and simmer until rice is cooked through, stirring occasionally, about 25 minutes.
Stir in up to 1 cup water or more beef broth to thin as desired (it will thicken as it rests and become almost like a stew), then stir in lemon juice and parsley.