In a skillet, on medium high heat, saute your onions until translucent and then add in your garlic. Turn off heat and put onion mixture in a bowl. Reserve the skillet for later.
After you've grated your potato, squeeze out the excess water with a paper towel and place the drained potato in the bowl with the onion mixture.
Add in the basil, garlic powder, salt, pepper and cheese.
Combine and mix well.
Form the mixture into small patties and set aside on a plate.
In the same skillet that you cooked your onions and garlic in, add some olive oil and place on medium high heat.
Place about 2-3 patties in the skillet (depending on what size your skillet is) and cook the patties until they're cooked through and brown on both sides.