Preheat the 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, sliced carrots, celery, and mushrooms. Cook for 5-6 minutes until vegetables are tender.
Sprinkle the flour over the vegetables and stir well to coat. Cook for 1-2 minutes to remove the raw flour taste.
Gradually add chicken broth while stirring continuously to avoid lumps.
Add milk, dried thyme, salt, black pepper, and paprika. Stir and cook until the sauce thickens, about 5 minutes.
Add cooked chicken, frozen peas, and cooked rice to the sauce. Stir to combine evenly.
Transfer the mixture to a greased 9×13 inch casserole dish.
Sprinkle shredded cheddar cheese evenly over the top.
Bake uncovered for 25-30 minutes until the cheese is melted and bubbly.
Remove from oven and let cool for 5 minutes before serving.