Preheat oven to 350°F (175°C) and grease a casserole dish.
In a large skillet, heat the olive oil over medium heat. Add the onion and garlic and cook until softened, about 5 minutes.
Add the carrots and peas to the skillet and cook for an additional 5 minutes.
In a large bowl, combine the cooked turkey, cooked rice, vegetable mixture, cream of mushroom soup, chicken broth, dried thyme, salt, and black pepper. Mix well.
Transfer the mixture to the greased casserole dish and sprinkle the shredded cheddar cheese on top.
Bake in the preheated oven for 30-40 minutes, until the cheese is melted and the casserole is heated through.
Remove from the oven and let cool for a few minutes before serving.
Enjoy!