Be sure to cook your rice if you haven’t already (if you are just reading this and just now realized you don’t have any cooked rice and don’t want to wait, consider switching to quinoa, which cooks much more quickly than brown rice. Instant brown rice also works in a pinch).
Preheat the oven to 350 degrees F. Coat a large casserole dish (9x13 inch or similar) with nonstick spray and set aside.
In a Dutch oven or large, deep skillet, heat the olive oil over medium high. Add the onion, green bell pepper, and red bell pepper. Sauté until slightly softened, about 5 minutes.
Add the beef, chili powder, cumin, salt, black pepper, and cayenne pepper. Continue to sauté until the beef is cooked through and no longer pink, about 4 to 5 minutes. Add the garlic and cook just until fragrant, about 1 additional minute.
Remove from the heat. Stir in the rice and Greek yogurt until evenly combined. Taste and adjust seasoning as desired.
Assemble the casserole: Spread the beans into an even layer in the prepared baking dish.
Sprinkle ¼ cup cheddar cheese and ¼ cup mozzarella cheese over the beans.
Scatter the tomatoes with green chilis over the top.
Spoon the rice and ground beef mixture on top of the tomatoes, spreading it into an even layer.
Top with remaining ½ cup cheddar and ½ cupmozzarella.
Bake the casserole, uncovered, until the cheese is melted and the casserole is hot, about 15 minutes.
Turn the oven to broil, then continue cooking until the cheese is lightly browned, about 3 to 4 additional minutes, watching carefully so that the cheese does not burn.
Let rest 5 minutes, sprinkle with chopped cilantro and green onions, and serve.