1. Finely chop onion and mince garlic. In a small skillet, heat vegetable oil and saute onion and garlic until soft (about 7 minutes). Set aside to cool.
2. If you use defrosted broccoli, remove excess moisture with paper towels (for fresh broccoli, blanch it for 2 minutes). Chop into bite size pieces. Transfer to a large bowl.
3. Add breadcrumbs, lightly beaten eggs, Parmesan cheese, Cheddar cheese, onion and garlic to the bowl. Season with salt and pepper to taste (not too much since cheese already has salt). Mix until combined.
4. Preheat oven to 400 degrees F (200 degrees C). Line a baking sheet with aluminum foil and brush it with vegetable oil.
5. Form the mixture into patties. To shape perfect patties use a lid (mine comes from a large mayonnaise jar). Cover the lid with plastic wrap (this will help to easier remove the patty). Fill it with the mixture, pressing it down lightly. Flip the patty out and repeat with the rest of the mixture.
6. Transfer patties to the prepared baking sheet.
7. Bake in the preheated oven for 15 minutes.
8. Flip and bake for another 10 minutes.