Place the potato in a steamer and cook for 8 minutes.
Add the broccoli to the steamer and steam the vegetables for an additional 2 minutes, or until they are fork tender. Then, remove everything from pot and allow them to cool.
In a large bowl, mash the potatoes and chop the broccoli florets into bite-size pieces.
Add the broccoli, cheese, panko, egg, salt, garlic and onion powder and combine.
Place the remaining panko in a separate bowl.
Roll 2 tablespoons of the mixture into balls, coat them in the panko and then shape each one into a small patty.
Heat oil in a skillet over medium heat. Place the patties in the skillet and press down with a spatula to flatten a little. Pan-fry for 3-4 minutes on each side until golden brown.