Preheat the oven to 375°F (190°C).
In a large oven-safe skillet or casserole dish, heat the olive oil over medium heat.
Add the diced onion and cook for 3-4 minutes until softened.
Add the minced garlic and cook for 30 seconds until fragrant.
Add the chicken pieces to the skillet and cook for 5-6 minutes until they are lightly browned but not fully cooked through.
Stir in the uncooked rice, frozen peas and carrots, and chopped broccoli.
Pour in the chicken broth and water, then stir to combine all ingredients evenly.
Add the dried thyme, paprika, salt, and black pepper, stirring to distribute the seasonings.
Spread the mixture evenly in the skillet or casserole dish.
Cover the dish tightly with aluminum foil and bake in the preheated oven for 35 minutes.
Remove the casserole from the oven and carefully remove the foil.
Stir in the sour cream and half of the shredded cheddar cheese.
Sprinkle the remaining cheddar cheese evenly on top.
Return the casserole to the oven, uncovered, and bake for an additional 10 minutes until the cheese is melted and bubbly.
Remove from the oven and let it rest for 5 minutes before serving.