Preheat oven to 350˚. Cook Elbow pasta per box directions.
In cast iron skillet melt butter over a medium heat. Add in carrots, celery and onions. Cook until softened, about 5 minutes.
Mix in flour and cook for about 1 minute constantly stirring. Slowly whisk in milk and broth until smooth. Bring to a boil turn down heat and allow to simmer until thickened. About 4-5 minutes.
Add all seasonings and mix completely. Turn off heat and mix in 1/2 cup of cheddar cheese. Mix until it is melted all the way in.
In large bowl mix pasta, chicken and peas. Then add into skillet with cheese sauce. Then lay American cheese slices on top.
Bake for 10 minutes. Take out of oven, top with crackers and the rest of the cheese. Then put back in the oven for another 10 minutes until cheese is melted.