Preheat oven to 375°F (190°C).
Heat olive oil in a large skillet over medium heat.
Add diced onion and cook for 3-4 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Add ground turkey to the skillet and cook until browned, breaking it up with a spoon, about 6-8 minutes.
Add diced red bell pepper, zucchini, and sliced mushrooms to the skillet. Cook for 5 minutes until vegetables are tender.
Stir in drained diced tomatoes, cooked brown rice, dried Italian seasoning, salt, and black pepper. Cook for 2 more minutes, stirring to combine.
Transfer the turkey and vegetable mixture to a 9×13 inch baking dish and spread evenly.
Sprinkle shredded mozzarella and cheddar cheese evenly over the top.
Cover the baking dish with aluminum foil and refrigerate if making ahead, or bake immediately.
To bake from refrigerated, preheat oven to 375°F (190°C). Bake covered for 25 minutes, then remove foil and bake an additional 15 minutes until cheese is melted and bubbly.
Remove from oven and let stand for 5 minutes before serving.