Preheat oven to 400F. Grease a 13x9 pan with cooking spray. Set aside.
Heat a large skillet over medium-high. Season chicken with 1/4 tsp each of salt and pepper. Coat skillet with cooking spray and sear chicken on both sides until browned, about 2 minutes each. Transfer chicken to a plate. Remove skillet from heat. (Skip this step if using pre-cooked chicken)
In a medium bowl, mix together chicken broth and stuffing mix. Set aside while you prepare the rest of the recipe. The stuffing cubes should absorb nearly all of the broth after a few minutes.
Chop broccoli into bite-sized pieces. In the cooled skillet, whisk together almond milk, cornstarch, garlic powder, onion powder, mustard, and remaining 1/4 tsp each of salt and pepper. Whisk well until combined, then return skillet to medium-high heat.
Continue whisking until the sauce starts to bubble and thicken, about 5 minutes. Once the sauce is pretty thick, remove from heat and whisk in cheese. Continue whisking until the cheese has fully melted into the liquid. If you like well done broccoli, add it into the sauce, return to heat, and cook for about 2-3 minutes.
Stir broccoli and chicken into the sauce. Pour into prepared pan and evenly distribute the broccoli and chicken. Sprinkle stuffing mixture in a layer over the top.
Bake uncovered for 30-40 minutes, or until stuffing is browned on top.