Fry the bacon in a large skillet over medium heat until crisp. Remove to paper towels to drain, then crumble and set aside. Pour off bacon grease, reserving about 1 tablespoon in the pan.
Fry the cabbage in the bacon grease over medium heat until cabbage is tender, or to your desired degree of doneness. Remove from the heat and season with salt and pepper. Top with shredded cheese and crumbled bacon.