Preheat your oven to 350°F and position a rack in the center. While the oven heats, grease a 9-inch round cake pan (or 8x8-inch square pan) generously with butter or oil, then line the bottom with parchment paper. This dual approach prevents sticking and makes cake removal effortless.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, and ground nutmeg. Whisking aerates the flour and distributes the leavening agents evenly, which ensures a tender, evenly-risen cake. Set this mixture aside.
In a large bowl, whisk together the room-temperature eggs, sugar, olive oil, yogurt, and vanilla until smooth and well combined, about 1-2 minutes. The room-temperature eggs emulsify more easily with the oil, creating a more tender crumb. I find that starting with the eggs and sugar, whisking them together first, then adding the oil slowly while whisking helps create the smoothest batter.
Add the dry ingredient mixture from Step 2 to the wet ingredient mixture from Step 3, folding gently with a spatula until just combined—stop as soon as you don't see streaks of flour. Overmixing develops too much gluten and results in a dense, tough cake. Pour the batter into your prepared pan and smooth the top lightly.
Bake for 50-55 minutes, until a toothpick inserted in the center comes out with just a few moist crumbs. The cake should be golden brown and spring back when lightly touched. Let the cake rest in the pan for 10 minutes (this allows the structure to set), then turn it out onto a wire cooling rack to cool completely, about 1-2 hours.
Once the cake is completely cooled, dust the top generously with sifted powdered sugar. Slice and serve with a dollop of Greek yogurt and fresh fruit. The tang of the yogurt and sweetness of the fruit complement the subtle nutmeg and vanilla flavors beautifully.