Preheat oven to 400 degrees F. Line a large, rimmed baking sheet with foil and spray with cooking spray.
In a shallow bowl, stir together breadcrumbs, Parmesan, and garlic powder.
Melt butter in a separate bowl.
One at a time, dip a chicken breast in the butter and then dredge the chicken breast in the breadcrumb mixture. Place the chicken on the prepared baking sheet. Repeat with remaining chicken.
Bake for 25 minutes, or until chicken is almost cooked through and crust is golden brown.
While the chicken is in the oven, toss broccoli florets with olive oil and season with salt and pepper. Set aside.
Remove chicken from oven.
Add the broccoli to the sheet pan in a single layer around the chicken. Return the pan to the oven and bake for about 10-15 more minutes, or just until the broccoli is tender and the chicken reaches an internal temperature of 165 degrees F.