Preheat the oven to 350°F (180°C). Meanwhile, melt the butter and set aside.

In a large bowl, whisk the eggs with the sugars. Add the Greek yogurt and mix well.

Pour in the cooled melted butter and stir again.

Add the flour and baking powder, mixing until combined. Finally, add the vanilla extract and mix.

Pour the batter into a silicone or greased and floured cake pan. Bake for 30–35 minutes at 350°F (180°C), depending on your oven. Check doneness by inserting a knife into the center—it should come out clean.

Let the cake cool before removing it from the pan.