While you're gathering ingredients, dice the onion into 1/2-inch pieces and shred the cabbage into 1-inch strips—doing this prep work first means you won't be juggling multiple tasks once the meat hits the pan. Heat a large skillet over medium-high heat and add the ground beef, breaking it apart as it cooks for about 5-7 minutes until it's completely browned. Drain excess fat from the skillet, leaving just enough to coat the bottom.
Add the diced onion to the browned beef and cook for 3-5 minutes, stirring occasionally, until it becomes soft and slightly translucent. This step develops the base flavor of the dish. While the onion cooks, combine all the spices in a small bowl: chili powder, garlic powder, smoked paprika, salt, and pepper. I find mixing spices separately ensures they distribute evenly throughout the dish instead of creating clumps.
Add the shredded cabbage to the skillet with the beef and onions, stirring to combine. Pour in the diced tomatoes and tomato sauce, then sprinkle the spice mixture over everything and stir well to distribute the flavors evenly. The cabbage will seem like a lot at first, but it will wilt down significantly as it cooks.
Cover the skillet and reduce heat to medium, simmering for 15-18 minutes until the cabbage is tender and the flavors have melded together. Remove the lid and evenly distribute the shredded cheese over the top of the casserole. I prefer Tillamook Sharp Cheddar because it melts beautifully and adds a richer flavor than milder cheeses. Cover again and cook for 2-3 minutes until the cheese is completely melted and bubbly.