Coarsely shred the zucchini (about 4 cups) in a medium bowl, add salt and let it stand for 15 minutes. Squeeze excess moisture with your hands.
Squeeze out the excess water with your hands.
Add the eggs, parmesan cheese, and minced garlic. Combine everything until you get a batter.
In a large skillet over medium heat, add 2 tablespoons of butter.
Take about 2 tablespoons of the zucchini mixture and flatten them in the skillet to form a patty. Add as many patties as you can to the skillet, but avoid overcrowding.
Cook until golden brown on each side, turning once. This should take around 6 to 8 minutes.
Repeat until the mixture is finished. Add more butter to the skillet if needed. Enjoy hot!