Preheat the oven to 400 degrees Fahrenheit. Coat a 2-quart (7 x 11-inch) baking dish with butter.
Heat the olive oil in a large, deep pan set over medium heat. Add the ground beef, onion, salt, and pepper to the pan; cook, breaking up the meat with a wooden spoon, until the beef is browned, about 5 minutes.
Add the garlic, paprika, thyme, and cayenne, and continue to cook while stirring for 30 seconds.
Add the chopped cabbage and the drained tomatoes, and continue cooking, stirring often, for approximately 5 minutes, or until the cabbage is soft.
Remove the pan from the heat and mix in 1 cup of the shredded cheese.
Transfer the mixture to the prepared baking dish with a slotted spoon. Sprinkle the remaining cheese on top.
Bake uncovered for 20 to 30 minutes until bubbling and the cheese is browned.
Before serving, let the dish rest for 10 minutes.