Step 1
Spray a skillet with cooking spray and place over medium heat; cook chicken in the hot skillet until no longer pink in the center and the juices run clear 6 to 8 minutes per side. Set chicken aside.
Step 2
Preheat oven to 350 degrees F (175 degrees C). Spray a 9x13-inch casserole dish with cooking spray.
Step 3
Place broccoli in the prepared casserole dish.
Step 4
Melt 3 tablespoons butter in a saucepan over medium heat; stir flour into the melted butter until combined and thickened 3 to 5 minutes. Slowly pour in chicken stock and milk stirring constantly; continue cooking and stirring until sauce is thickened 5 to 10 more minutes.
Step 5
Stir onion red bell pepper serrano chile pepper habanero pepper and carrot into the sauce; simmer until vegetables are slightly softened 5 to 10 minutes.
Step 6
Cut the cooled chicken into cubes and sprinkle over broccoli. Pour sauce over chicken and broccoli.
Step 7
Heat 1 teaspoon butter in a skillet over medium heat; cook and stir mushrooms until tender 5 to 10 minutes. Spoon over sauce layer in the casserole dish. Sprinkle bread crumbs and Parmesan cheese over mushroom layer.
Step 8
Bake in the preheated oven until cooked through and bubbling about 30 minutes. Turn on the oven's broiler; broil casserole until topping is browned 2 to 4 minutes.
Step 9
Spoon casserole into 4 bowls and sprinkle 1/4 cup arugula atop each serving.