Season the chicken with salt and pepper. Place a large skillet over medium-high heat and pour in the oil. Once the oil is hot add the chicken and broccoli, and cook until the chicken is cooked through. Drain any liquid from the skillet.
Spread the chicken and broccoli out in the bottom of a 9-inch x 13-inch casserole dish.
Mix together the cream of chicken soup, sour cream, half and half, 1 cup of cheddar cheese, garlic powder, and salt in a mixing bowl until well combined.
Pour the sauce over the chicken and broccoli and mix everything together. Sprinkle with the remaining cup of cheddar cheese.
In a small bowl, mix together the butter and bread crumbs. Sprinkle evenly over the cheese.
Bake for 20-25 minutes until the cheese is melted, the bread crumbs are golden, and the sauce is bubbly. Remove from the oven and serve warm.
Notes
You can use fresh or frozen broccoli. If using frozen, thaw it before cooking.