Preheat oven to 400F (200C). Line a baking sheet with parchment paper.
Grate cheeses using the small holes of the grater.
Cut broccoli florets in very small pieces and transfer to a large bowl. Add cheese, onion, garlic, oats, breadcrumbs, salt and pepper into the bowl. Add 2 eggs and mix to combine. If still too dry add another egg.
Use an ice cream scoop to take equal portions of broccoli and cheese mixture and form into balls. Place the balls on the prepared baking sheet and sprinkle with a bit of vegetable oil over the top.
Bake for 25 -30 minutes until slightly golden.
Serve with your favorite dipping sauce or as a side dish.