In a straight-sided skillet, heat 1 inch of vegetable oil to 360 degrees. Grate the zucchini on the medium holes of a box grater onto a kitchen towel. Tightly wrap the zucchini in the towel, and wring out as much liquid as possible. Beat the eggs in a large bowl. Stir in the zucchini, breaking up any clumps with a fork. Stir in the parsley and lemon zest.

Sift together the flour, baking powder, and salt. Stir into the egg mixture until just combined—don’t overmix.

Brush a soup spoon with vegetable oil, and with it drop dollops of batter into the oil, patting the fritters lightly with the back of a spatula to flatten slightly. Fry, turning once, until golden on both sides and cooked through, about 2 minutes per side. Fry them in batches. The fritters are cooked when a fork inserted in the center comes out clean. Drain cooked fritters on paper towels, and season lightly with salt. Serve fritters right away, with lemon wedges.