To begin, shred up the zucchini and toss it in a mixing bowl.
Add in the fresh lemon zest, salt, pepper, parsley, garlic, and eggs. Stir this all together, so that everything is coated with the egg.
Sprinkle the flour all over the mixture and then stir it all in. Mix until there are no lumps of flour.
In a skillet, heat about a quarter cup or so of oil over medium heat. You want the bottom of the skillet to have a thin layer of oil. When the oil is nice and hot, but not smoking, scoop the mixture by ¼ cups at a time into the oil. Allow it to sit there and cook for 2-3 minutes, until it is golden on the bottom.
Carefully turn the fritter over and cook it on the other side until golden, around 2-3 minutes again.
Place the cooked fritters on a platter lined with paper towels and repeat with the remaining batter.
Keep the fritters that are already cooked warm by setting your platter in a warm (not hot) oven while the others cook.