Preheat the oven to 375°F (190°C).
Heat olive oil in a large skillet over medium heat.
Add diced onion, minced garlic, diced green bell pepper, and diced carrots to the skillet. Sauté for 5 minutes until vegetables are softened.
Add rinsed rice to the skillet and stir to combine with the vegetables.
Pour in chicken broth and water, then add dried thyme, dried oregano, salt, and black pepper. Stir well.
Bring the mixture to a boil, then remove from heat.
In a large casserole dish, combine the cooked chicken breast and frozen peas.
Pour the rice and vegetable mixture over the chicken and peas. Stir gently to combine evenly.
Cover the casserole dish tightly with aluminum foil.
Bake in the preheated oven for 35 minutes.
Remove the foil and sprinkle shredded cheddar cheese evenly over the top.
Return the casserole to the oven uncovered and bake for an additional 10 minutes, or until the cheese is melted and bubbly.
Remove from oven and let stand for 5 minutes before serving.