Preheat oven to 400 degrees F. Line 2 baking sheets with foil and spray with cooking spray.
Pierce sweet potato with a fork many times. Place in microwave and microwave for 6-8 minutes, until soft and cooked through. Let cool for about 10 minutes.
Place chopped broccoli in a microwave safe bowl. Add 3 tablespoons of water and microwave for 5-6 minutes, until lightly steamed. Once steamed, roughly chop the broccoli into very small pieces. You can also place it in a large food processor and pulse until coarsely chopped.
In a large bowl, mash the sweet potato.
Add the broccoli, eggs, breadcrumbs, and cheese, and mix well. Stir in the garlic powder and onion powder, if desired.
Form into small patties and place onto prepared baking sheets.
Bake in preheated oven for 20-25 minutes.