In a large mixing bowl, combine the broccoli, 1½ cups of cheddar, Parmesan, eggs, half the panko, garlic, onion, parsley, oregano, and red pepper flakes.
Season with salt and pepper.
Mix thoroughly and refrigerate for 30 minutes.
Shape and Coat:
Preheat the oven to 400°F (200°C).
Line a baking sheet with parchment paper.
Place the remaining panko in a shallow dish.
Form the broccoli mixture into 1½-inch balls using damp hands.
Roll in panko to coat.
Bake:
Place balls on the baking sheet and spray lightly with olive oil.
Bake for 20-25 minutes, turning halfway through, until golden brown.