Bring a large pot of water to a boil. Add the broccoli and blanch for 1-3 minutes. *see notes
Rinse with cold water to stop the cooking. Drain well, pat dry, and set aside.
Preheat the oven to 350° and grease a 9 x 13-inch baking dish with cooking spray.
Season chicken with salt and pepper, to taste.
Heat 1 tbsp of olive oil in a large skillet over medium heat. Sauté the chopped chicken until no longer pink, about 4-5 minutes, stirring occasionally. Remove the chicken from the skillet and set aside.
Add the butter and remaining olive oil to the skillet. When butter is melted, add the garlic and onion and cook until soft. Sprinkle the flour and whisk until smooth. Stir in broth, milk, and sherry and bring to a boil while whisking.
Remove from heat and stir in half of the cheddar cheese, and season with additional salt and pepper, to taste. I use about a teaspoon of salt and half a teaspoon of pepper.
Arrange the blanched broccoli in a casserole dish and pour half of the sauce over the broccoli.
Arrange the chicken on top and cover with remaining sauce. Sprinkle the remaining cheddar cheese, grated parmesan and top with breadcrumbs.
Spray a little oil on top.
Bake 30 minutes, serve hot.