Brown the ground beef in a large skillet over medium-high heat, breaking it up as it cooks, until fully browned through.
Add the peppers and onions directly to the skillet with the beef. Cook, stirring occasionally, for 4 to 5 minutes until they begin to soften. Drain off the excess grease.
Stir in the stewed tomatoes, tomato paste, salt, pepper, garlic powder, onion powder, red pepper flakes, and thyme until well combined. Cover and simmer over medium-low heat for 20 minutes, stirring occasionally.
Turn off the heat. Microwave the rice pouch according to package directions, then stir the cooked rice into the beef and pepper mixture.
Stir in 1½ cups of the shredded cheddar until fully incorporated into the warm filling.
Transfer the mixture to a greased 9x13 inch casserole dish. Sprinkle the remaining cheddar evenly over the top. Dot the torn mozzarella chunks across the surface. If the dish looks very full, place it on a rimmed sheet pan to catch any drips.
Cover tightly with foil and bake at 350°F (175°C) for 30 minutes. Uncover and bake for 10 more minutes, then switch on the broiler for the last 2 minutes, or until the top is bubbly and golden. Watch closely during the broil.
Remove from the oven and let rest for 5 minutes before serving. This helps the casserole hold together and makes for cleaner portions.