Preheat the oven to 425°F and lightly grease a rimmed baking sheet with 1 tablespoon of the olive oil.
Place the chicken breasts in the center of the prepared baking sheet in a single layer.
Arrange the broccoli florets around the chicken on the baking sheet.
Drizzle the remaining 1 tablespoon of olive oil over the broccoli and chicken, then season everything evenly with the kosher salt and garlic powder.
Bake until the chicken is cooked through and a thermometer inserted into the thickest part reads 160°F, about 25 to 30 minutes.
While the chicken bakes, stir together the minced garlic, grated Parmesan, and chopped parsley in a small bowl.
Remove the pan from the oven and evenly top each chicken breast with the garlic-Parmesan-parsley mixture.
Set the oven to broil and broil the pan until the cheese is melted and the broccoli is deeply browned, about 3 minutes—watch closely to prevent burning.
Remove the pan, tent the chicken loosely with foil, and let rest for 5 minutes before serving.