Preheat the oven to 425° F.In a large skillet, set over medium heat, add 2 tablespoons butter, the onion, and chicken. Cook until the chicken is seared, 5 minutes. Add 1 tablespoon of butter, the rice, cherry tomatoes, and thyme, and cook until toasted, 2-3 minutes. Add 3 cups of water and bring to a boil over high heat. Add the cayenne. Cover, and reduce heat to low. Cook, covered for 15 minutes until the rice is mostly cooked.Once the rice is cooked, stir in 1 cup of cheese. If needed, transfer the rice to an oven-safe casserole dish. Scatter the remaining 1 cup of each type of cheese over the casserole. Lay the sliced heirloom tomatoes on the cheese. In a bowl, mix the olive oil, garlic, and chili flakes. Spoon the oil over the tomatoes and season with salt and pepper. Bake for 10 minutes, until the cheese is melted. Switch the oven to broil and broil 1-2 minutes, until the cheese on top is becoming crispy. Serve warm with fresh basil.