Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper or lightly grease it with cooking spray or olive oil.
In a large mixing bowl, combine the chopped broccoli, cheddar cheese, breadcrumbs, Parmesan cheese, eggs, garlic powder, onion powder, salt, black pepper, and red pepper flakes if using. Mix until all ingredients are well combined.
Using your hands or a spoon, form the mixture into small balls or patties, about 1 to 1.5 inches in diameter, and place them on the prepared baking sheet.
Bake in the preheated oven for 15-20 minutes, or until the bites are golden brown and firm to the touch.
Remove from the oven and let cool for a few minutes before serving.