Preheat the oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish or similar casserole dish.
Warm a large skillet over medium heat. Add butter or olive oil, then sauté the diced onion for 3–4 minutes until translucent.
Stir in the garlic and cook for 30 seconds until fragrant.
Add the broccoli (if using) to the skillet and cook 2–3 minutes to soften slightly. If using only frozen vegetables, you can skip this step and add them later.
In a large bowl, combine the cooked rice, turkey, sautéed onion mixture, frozen peas and carrots, 1.5 cups of the shredded cheese, cream of mushroom soup, sour cream, and milk or broth.
Season with thyme or Italian seasoning, garlic powder, onion powder, salt, and pepper. Stir until everything is evenly coated.
The mixture should be creamy but not soupy. If it seems dry, add a splash more milk or broth.
Transfer the mixture to the prepared baking dish and spread it into an even layer.
Top with the remaining 1/2 cup shredded cheese. If you like a crunchy finish, toss the crushed crackers or panko with a teaspoon of melted butter and sprinkle over the top.
Bake uncovered for 25–30 minutes, until the casserole is hot, bubbly around the edges, and the top is golden.
Let it rest for 5–10 minutes before serving.
Garnish with chopped parsley or chives for a fresh finish.