While oven is pre-heating to 400, prepare your baking sheet. You will want to line it with foil and then lightly grease it.
Add oil to a medium sauté pan and heat over medium heat. Add onions and garlic, and salt and pepper to taste. Watch for doneness... you want to cook the onions until just tender. Set aside.
Remove as much moisture as possible from your broccoli. This will help you get the best texture in the finished dish. Add the dry broccoli, panko, cheeses, egg and a bit of salt and pepper to a large bowl. Combine well.
Form broccoli mixture into small-ish patties and carefully place them on your baking sheet. Bake for 30 minutes, flipping the patties half way through. They are done when they appear golden and crispy!