Preheat the oven to 400°F, and grease or lightly spray a 9-inch pie dish. (Alternatively, a 9-inch round cake pan or 8-inch square baking dish could be used.)
In a clean tea towel, squeeze the shredded zucchini to remove the excess moisture. Add the zucchini to a mixing bowl, followed by the onions, chives and cheese. Using a fork, whisk in the eggs. Then sprinkle the flour, baking powder, salt and pepper overtop, and stir to incorporate. Finally, stir in the milk.
If using, thinly slice the tomato, discarding any clumps of seeds, and arrange the slices in an even layer over the bottom of the prepared baking dish. (You can cut the slices in half to more evenly cover the surface, but some gaps are fine.) Sprinkle the Parmesan evenly over the top, and bake 30-35 minutes or until the center is cooked through and the surface is deeply golden.
Let the pie stand for 5-10 minutes before serving. Leftovers may be cooled, covered and refrigerated for 4-5 days and reheat well in a 325°F to 35O°F oven.