Heat olive oil in a large oven-safe pot or Dutch oven over medium heat.
Add diced onion and cook until softened, about 4 minutes.
Add minced garlic and cook for 1 minute until fragrant.
Add chicken pieces to the pot, season with salt, pepper, and dried thyme. Cook until chicken is lightly browned but not fully cooked through, about 5 minutes.
Add rinsed rice to the pot and stir to coat with oil and mix with chicken and vegetables.
Pour in chicken broth and stir to combine.
Add diced carrots and frozen peas, stirring gently to distribute evenly.
Bring the mixture to a boil, then cover the pot with a lid and reduce heat to low.
Simmer covered for 25-30 minutes, or until rice is tender and liquid is absorbed.
Remove the lid and sprinkle shredded cheddar cheese evenly over the top.
Cover again and cook for an additional 5 minutes until cheese is melted.
Remove from heat and let the casserole rest for 5 minutes before serving.