Preheat the oven to 375°F (190°C).
Heat olive oil in a large skillet over medium heat.
Add diced onion and minced garlic to the skillet and sauté for 3-4 minutes until softened.
Add ground beef to the skillet and cook, breaking it up with a spoon, until browned and no longer pink, about 6-8 minutes.
Drain excess fat from the skillet if necessary.
Add diced carrots and green bell pepper to the skillet and cook for 3 minutes, stirring occasionally.
Stir in the uncooked rice, frozen peas, diced tomatoes with their juice, beef broth, dried oregano, dried basil, salt, and black pepper.
Bring the mixture to a boil, then remove from heat.
Transfer the beef and rice mixture into a 9×13 inch casserole dish and spread evenly.
Cover the casserole dish tightly with aluminum foil.
Bake in the preheated oven for 35 minutes.
Remove the foil and sprinkle shredded cheddar cheese evenly over the top.
Return the casserole to the oven and bake uncovered for an additional 10 minutes, or until the cheese is melted and bubbly.
Remove from the oven and let stand for 5 minutes before serving.