To the warm pan, add the ground meat, onions, garlic, and celery. Sauté until the meat is fully browned.
Turn off the heat and quickly stir in the tomatoes. Transfer mixture to a casserole dish approximately 10×7 inches.
In a food processor, blend together the cauliflower, cream, cheeses and thyme until you have a mixture that more closely resembles mashed potatoes than riced cauliflower.
Spread the cauliflower over the meat in the casserole dish.