Step 1: Heat olive oil in a large Dutch oven or stockpot over medium heat. Add the chopped onion and cook until softened and translucent, about 5-7 minutes.
Step 2: Add the minced garlic and tomato paste to the pot. Cook for 1-2 minutes, stirring constantly, until the tomato paste darkens slightly and becomes fragrant.
Step 3: Add the ground beef and ground pork to the pot. Break up the meat with a spoon and cook until browned, about 8-10 minutes. Drain any excess fat.
Step 4: Stir in the smoked paprika, dried dill, dried marjoram, salt, and black pepper. Cook for another minute, allowing the spices to become fragrant.
Step 5: Add the chopped green cabbage, crushed tomatoes, beef broth, Worcestershire sauce, and brown sugar (or maple syrup) to the pot. Stir well to combine all ingredients, making sure the cabbage is submerged in the liquid.
Step 6: Bring the soup to a boil, then reduce the heat to low, cover, and simmer for 25-30 minutes, or until the cabbage is tender.
Step 7: Stir in the uncooked white rice. Continue to simmer, covered, for another 15-20 minutes, or until the rice is cooked through and tender. Stir occasionally to prevent the rice from sticking to the bottom of the pot.
Step 8: Taste the soup and adjust seasonings as needed. You might want a pinch more salt, pepper, or a touch more sugar to balance the acidity.
Step 9: Ladle the hot soup into bowls. Garnish with a dollop of sour cream or plain Greek yogurt and a sprinkle of fresh chopped parsley or dill, if desired.