Prepare rice in microwave according to instructions.
Cut off tops of pepper; remove seeds and white membranes. Discard stems; dice tops fine. Crumble ground beef into a microwave safe colander set in a shallow 1 1/2 quart casserole dish. Add the diced pepper tops, onion, and carrot to colander.
Cover loosely with waxed paper, microwave on high 4 to 6 minutes, stirring once, until meat is no longer pink and vegetables are tender. Drain any liquid left in the colander, then put meat mixture in a bowl. Stir in rice, 3/4 cup cheese, tomato sauce, and the salt and pepper.
Spoon that rice mix into the peppers in the casserole. Cover loosely with waxed paper. Microwave on high for 11 to 14 minutes, rotating dish three times, until peppers are crisp, tender, and hot. Spoon remaining tomato sauce on top of the peppers, then sprinkle with remaining cheese. Cover and let stand for 6 to 8 minutes until sauce is hot, cheese is melted, and pepper is almost tender.