Preheat the oven to 350 degrees and grease a baking sheet.
Heat the olive oil in a large skillet over medium-low heat. Add the diced onion and cook for a few minutes, until translucent. Add the garlic and cook for another 30 seconds. Add the spinach to the skillet and cover. Cook for a minute, then lift the cover and stir the spinach. Cover it again and cook for another minute. Repeat this until the spinach is wilted. Turn off the heat, add the salt and nutmeg, and stir to season evenly.
Transfer the spinach to a bowl and add the egg and feta. Stir everything together, then set the spinach mixture aside.
In the bowl of a stand mixer, stir together the flour, baking powder, and salt. Add the eggs, olive oil, and ¼ cup of water. Mix in the stand mixer until combined. Add more water one tablespoon at a time until the dough comes together easily. If you add too much water and the dough gets sticky, put in a little more flour.
Roll the dough into a rectangle on a floured work surface. It should measure about 10 by 16 inches. Spread the spinach mixture on the dough to make an even layer. Then carefully roll it up so you have a 16-inch long log. Cut the log into 16 pieces that are about an inch wide. Carefully transfer each pinwheel onto the prepared baking sheet. Sprinkle the pinwheels with the grated parmesan.
Bake the pinwheels for about 12 minutes, or until the parmesan is melted and the pinwheels are beginning to turn brown on the bottom. Serve warm or at room temperature. These taste best right out of the oven.