Place a couple sheets of paper towel on a cutting board or work surface, and grate your zucchini onto it using the coarse side (the big holes) of a box grater. Sprinkle with salt and let sit a few minutes. Place another paper towel on top, gather up the zucchini inside the towels and wring out as much liquid as you can - if you like, squeeze it into a bowl and use the liquid in soup or pasta. (It will be salty.)

Transfer the shredded zucchini to a bowl, add the feta, then stir in the egg and some freshly ground black pepper, tossing to combine it all. In a small bowl, stir together the flour and baking powder, then stir it into the zucchini mixture.

In a large, heavy skillet, heat a generous drizzle of oil over medium-high heat. Drop the batter in large spoonfuls, then flatten with the spoon until they are 2-3" in diameter. Cook for a few minutes, until the bottoms are golden, then flip and cook for another couple minutes on the other side. If they are browning too quickly, turn the heat down a bit. Transfer to a plate lined with a paper towel. If you like, keep them warm in a 250F oven while you cook the rest. Serve immediately, while still warm.