Grate the zucchini on the large holes of a box grater. Toss with 3/4 tsp kosher salt in a colander and rest for 10 minutes. Wrap in a clean kitchen towel and squeeze thoroughly to remove as much liquid as possible.

Whisk the egg in a large bowl. Stir in the flour, cornstarch, Parmesan, scallions, garlic, black pepper, baking powder, and remaining 1/4 tsp salt. Fold in the drained zucchini until evenly combined.

Heat a 12-inch heavy skillet over medium to medium-high heat. Add about 2 tbsp oil. Once shimmering, scoop about 3 tbsp batter per fritter into the skillet and flatten into roughly 3-inch rounds about 1/3 inch thick. Cook four at a time for 3 to 4 minutes, until deeply golden underneath.

Flip and cook for another 2 to 3 minutes, until the second side is golden and the centers are set. Transfer to a wire rack and repeat with the remaining batter, adding the rest of the oil as needed. Serve hot.