Place carrots in a heavy-duty zip-top plastic bag; seal. Place in a microwave-safe dish. Cut several slits in bag.
Microwave at HIGH 2 minutes; add broccoli and cauliflower, and seal bag. Microwave at HIGH 2 minutes or until vegetables are tender.
Melt butter in skillet over medium heat; add onion and garlic, and sauté 5 minutes.
Arrange one-third of vegetables in a lightly greased 2-quart baking dish. Spoon one-third of onion mixture over vegetables. Stir together cheeses; sprinkle 1/2 cup cheese mixture over onion mixture; sprinkle with one-third of pepper. Repeat procedure twice.
Bake at 350° for 25 minutes.