Heat the olive oil in a large pot over medium-high heat until shimmering, about 1-2 minutes. Add the ground beef and break it apart with a wooden spoon as it cooks, stirring occasionally until it's browned and no longer pink, about 4-5 minutes. Season with a pinch of salt and pepper as it cooks. Once the beef is browned, add the chopped onion and garlic, stirring constantly for 2-3 minutes until the onion becomes translucent and fragrant—this builds flavor by allowing the aromatics to cook in the rendered beef fat.

Add the chopped cabbage and sliced carrots to the pot, stirring well to combine with the meat mixture. Pour in the beef broth and tomato sauce, then add the rice, bay leaf, brown sugar, and smoked paprika. Season with a pinch of salt and pepper to taste. Bring the soup to a gentle simmer over medium heat, then reduce heat to medium-low and let it simmer uncovered for about 25 minutes, stirring occasionally. The soup is ready when the rice is tender and the vegetables are softened. I like to give it a stir every 7-8 minutes to prevent the rice from sticking to the bottom and to help the flavors distribute evenly throughout the soup.

Remove the bay leaf from the pot and discard it. Stir in the fresh parsley just before serving to brighten the flavors without losing its vibrant color from heat. Taste the soup and adjust the seasoning with additional salt and pepper as needed. Ladle into bowls and serve hot. I find that letting the soup sit for a few minutes before serving allows the flavors to meld together nicely.