Heat the olive oil in a large skillet over medium-high heat. Add the ground beef and break it apart with a wooden spoon as it cooks. Season with salt, pepper, and paprika while it browns.

Cook the beef for about seven to eight minutes, stirring occasionally, until no pink remains. Drain any excess grease from the skillet.

Push the beef to one side of the skillet, or transfer it to a plate temporarily. Add the diced onion to the same skillet and cook for three to four minutes until it turns soft and translucent.

Toss in the minced garlic and cook for another thirty seconds, stirring constantly.

Add the chopped cabbage directly into the skillet with the onions and garlic. Stir well, cover the skillet, and let the cabbage steam for about five minutes, stirring once halfway.

In a separate saucepan, melt the butter over medium heat until foamy. Whisk in the flour immediately and keep whisking for about a minute.

Slowly pour in the milk while whisking constantly to prevent lumps. Add the broth next and whisk until the sauce thickens, about four to five minutes.

Remove the saucepan from heat and stir in the sour cream until fully combined. Fold in one cup of shredded cheddar cheese until melted and smooth.

Preheat your oven to 375°F (190°C). In a large mixing bowl, combine the browned beef, the wilted cabbage mixture, and the creamy cheese sauce. Stir until evenly coated.

Transfer the mixture into a greased 9x13 inch baking dish, spreading it out evenly. Sprinkle the remaining half cup of cheddar cheese across the top.

Place the dish in the preheated oven and bake for 25 to 30 minutes until bubbling and golden on top.

Let the casserole rest for about five minutes before serving.