Heat the olive oil in a large pot or Dutch oven over medium-high heat. Add the ground beef and cook for 5 minutes, breaking it up as it cooks until it's no longer pink. Once browned, stir in the garlic powder, onion powder, oregano, and tomato paste, cooking for 1 minute to bloom the spices and deepen their flavor. This short cooking time allows the spices to become fragrant without burning.

Add the thinly sliced cabbage, tomato sauce, sugar, salt, pepper, and smoked paprika to the pot with the seasoned beef from Step 1. Stir well to combine everything evenly. The cabbage will release moisture as it cooks, which creates the braising liquid for the casserole.

Cover the pot and reduce the heat to medium-low. Cook for 15 minutes, stirring occasionally. The cabbage will begin to wilt and soften during this time, and the flavors will start to meld together. I like to stir halfway through to ensure the cabbage cooks evenly and the bottom doesn't stick.

Pour in the chicken stock and stir to combine. Increase the heat to medium-high and bring the mixture to a boil. Once boiling, stir in the rice, breaking up any clumps. The rice will absorb the flavorful liquid as the casserole finishes cooking.

Cover the pot and reduce the heat to low. Simmer for 15 minutes until the rice is tender and has absorbed most of the liquid. The rice will continue to cook gently in the residual heat and moisture, creating a cohesive, well-integrated casserole.

Remove the pot from heat and stir in the red wine vinegar. The vinegar adds a bright acidity that balances the richness of the beef and the earthiness of the cabbage. Cover and let the casserole sit for 5-7 minutes to allow the flavors to fully meld together. I find that this resting period makes a noticeable difference in how well all the flavors come together.