Preheat oven to 375 degrees F (190 C). Grease an 8x8-inch baking dish with olive oil.
Heat a large skillet over medium-high heat. Add the olive oil, and then add ground turkey to the skillet. Cook for about 3 minutes until it browns and starts to break apart.
Add onion, garlic, bell peppers, Italian seasoning, dried oregano, smoked paprika (if using), salt, and pepper to taste. Cook until vegetables are softened and fragrant, about 5 minutes.
Add diced tomatoes and tomato sauce to the skillet. Stir everything together and bring it to a simmer for about 3 minutes until the sauce thickens slightly. Add balsamic vinegar and stir once more.
Transfer the turkey mixture to the prepared baking dish. Spread cooked brown rice over the top of the turkey mixture. Sprinkle cheese on top of the rice.
Bake for 25-30 minutes until the cheese is melted and bubbly, and the casserole is cooked through. Serve hot with your favorite sides!