Heat the oven to 350°F. Grease a 9-inch springform pan lightly with baking spray or oil, and line the bottom with parchment.
Whisk together the yogurt, olive oil, sugar, eggs, and vanilla. Add the flour, baking powder, soda, salt, and nutmeg right into the liquids and stir just until no lumps remain.
Pour the batter into the cake pan and bake for 50 to 60 minutes, covering with foil at the end if the top is browning. When a tester comes out clean, transfer the cake to a cooling rack and let it cool for 10 minutes before removing it from the pan.