Pour olive oil into a pan and sauté the onion, garlic, carrot until tender; add frozen peas, salt and peppers and let simmer a few minutes more. Set aside.
Melt butter in a medium saucepan over low heat. Add flour and stir until smooth, this only takes a couple of minutes. Slowly pour in chicken stock, use a whisk to keep stirring until sauce thickens and has no lumps. Add salt and black pepper; stir. Add the cheddar cheese and continue to stir on low, until all the cheese is melted and the sauce is smooth and creamy.
Add the cooked rice, cooked chicken, seasonings, sautéed vegetables; mix together well. Pour into a greased 2 qt. casserole dish.
Spread remaining 1 cup cheddar cheese over the top and sprinkle with paprika (if desired).
Bake for 30 minutes uncovered or until the cheese on top melts.