Cook the carrots.
Melt butter in a pot over medium low heat.
Add flour to butter and stir.
Slowly add a little broth at a time, stirring constantly, until all broth added and thicken.
Lower heat, add cheese and stir until melted.
Remove from heat.
Add cooked chicken, cooked carrots, and pimentos.
Pour mixture into a greased 13x9 or casserole pan.
Add 1/4 c. butter to a pan and melt.
Add stuffing mix and stir.
Spread over top of chicken mixture.
Cook for 30-40 minutes at 375.