Preheat your oven to 400°F. Grease a 2-quart (7 X 11-inch) baking dish.
In a large, deep skillet, heat the olive oil over medium-high heat. Add the ground beef, onion, salt, and pepper. Cook until the beef is browned, about 5 minutes, stirring and breaking up the meat with a wooden spoon.
Add the garlic, paprika, thyme, and cayenne and cook for 30 seconds, stirring.
Add the drained tomatoes and chopped cabbage. Continue to cook, stirring often, until the cabbage is tender, about 5 minutes.
Turn the heat off and stir in one cup of the shredded cheese.
Using a slotted spoon, transfer the mixture to the prepared baking dish. Sprinkle it with the remaining cheese.
Bake, uncovered, until the casserole is bubbly and the cheese is browned, 20-30 minutes.
Let the casserole rest for 10 minutes before serving.
