Place the butter in the large oven safe saute pan and set over medium heat. Add the chopped onions, celery, and carrots. Saute for 5-8 minutes to soften.
Meanwhile chop the chicken breasts into small bite-size pieces. Once the veggies are softened, add the chicken, salt and thyme. Saute another 5 minutes to cook the chicken pieces partially through.
Add the broth and pasta. Stir to soak the pasta. Cover the pan and simmer for 6-7 minutes to cook the pasta through. Then remove the lid and stir in the frozen peas, shredded cheese, and cream. Salt and pepper to taste. Serve immediately or bake!
This step is entirely optional: Preheat the oven to to 350 degrees F. Sprinkle breadcrumbs over the top of the pasta. Bake for 15-20 minutes to develop a crusty top. You can transfer the pasta to a separate baking dish if you don't have an oven-safe saute pan.