Combine flour, baking powder, slat, and pepper. In a separate bowl, beat together the egg, milk, carrot, zucchini and green onion. Stir the wet ingredients into the dry until just combined.
Heat 1 tablespoon of oil in a skillet. Pour the batter by tablespoons into the hot oil. Cook until golden, about 2 minutes on each side. Add the remaining oil to the skillet as needed. Drain on paper towel.