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 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Add chicken pieces to the skillet and cook for 5 minutes until lightly browned but not fully cooked through.
In a large mixing bowl, combine the rinsed rice, chicken broth, water, frozen peas, diced carrots, diced bell pepper, chopped broccoli, dried thyme, dried oregano, salt, and black pepper. Stir to combine.
Add the partially cooked chicken, onion, and garlic mixture to the bowl and mix well.
Transfer the entire mixture to a greased 9×13 inch casserole dish and spread evenly.
Cover the casserole dish tightly with aluminum foil.
Bake in the preheated oven for 40 minutes.
Remove the casserole from the oven and carefully remove the foil.
Stir in the sour cream and half of the shredded cheddar cheese evenly into the casserole.
Sprinkle the remaining shredded cheddar cheese 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.