Heat a large skillet over medium-high heat. Cook and stir ground beef and onion in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease. Sprinkle flour over the beef mixture and toss to coat. Stir tomato sauce, green bell pepper, oregano, and chili powder through the beef mixture.
Season eggplant slices with salt and pepper; arrange over the beef mixture. Place a cover on the skillet and continue to simmer until the eggplant is tender, 10 to 15 minutes. Top with Cheddar cheese to serve.