Preheat your oven to 425°F (220°C).
In a large mixing bowl, combine the broccoli florets, olive oil, garlic powder, onion powder, salt, black pepper, and red pepper flakes. Toss until the broccoli is evenly coated.
Spread the broccoli mixture in a single layer on a baking sheet lined with parchment paper.
Bake in the preheated oven for 15 minutes.
Remove the baking sheet from the oven and sprinkle the cheddar and Parmesan cheeses evenly over the broccoli.
Return the baking sheet to the oven and bake for an additional 10-12 minutes, or until the cheese is melted and bubbly, and the broccoli is crispy.
Allow to cool for a few minutes before serving.