Trim off both ends of each zucchini, then either shred them on the coarse side of cheese grater, or slice them as thinly as you can manage. (If you have one, a mandolin, set to its thinnest setting, is ideal for the job.) Set aside.
In a large mixing bowl (or the bowl of a standing mixer) mix the flour, sugar and baking powder. Add the milk, vanilla extract and grated lemon zest until you have a smooth batter. Fold the shredded or sliced zucchini into the batter.
Butter a baking dish generously, then pour in the zucchini batter. Drizzle a bit of olive on top, then place in a hot (200C/400F) oven for about an hour, until cooked through and nicely browned on top.
While it's baking, check on your scarpaccia every 20 minutes or so. If it's getting a bit too brown for your liking, you can lower the oven temperature to 180C/350F. On the other hand, if towards the end of baking you find your scarpaccia isn't brown enough, you can run the cake under the broiler for a few minutes at the end.
Remove from the oven and set the baking pan on a rack. Let cool completely.
Serve your scarpaccia at room temperature, dusted with confectioner's sugar.