Preheat oven to 350. Grease a 9x13 pan. Remove the meat from the rotisserie chicken. Discard the skin and chop up the meat. Reserve any juice from the chicken.
Heat olive oil in a large skillet or pot. (Mine was a 6 quart skillet). Saute onion, celery and carrots until softened, about 10 minutes. Stir in garlic and cook for 1 minute. Stir in chicken, both rices, salt, pepper, garlic salt, and reserved juice from rotisserie chicken. Reduce heat to low.
In a separate saucepan, melt butter over medium high heat. Whisk in flour, salt and pepper until smooth. Slowly pour in chicken broth, whisking continuously. Whisk until thick and nearly boiling then stir in mozzarella cheese until melted. Pour cheese sauce into rice mixture. Stir until well incorporated, then transfer to the prepared 9×13 inch baking dish. Top with the shredded colby jack cheese and bake for 25-30 minutes until bubbly and cheese is melted through. Let set a few minutes before serving.