Preheat oven to 350°F. Grease a 9-inch springform pan with olive oil or butter, line the bottom with parchment paper, and set aside.
In a large bowl, whisk together the flour, baking powder, baking soda, and salt.
In another bowl, whisk the olive oil, eggs, sugar, lemon zest, lemon juice, yogurt, and vanilla until smooth and well combined.
Add the wet ingredients to the dry ingredients and mix until just combined. Be careful not to overmix.
Pour the batter into the prepared pan and smooth the top.
Bake for about 40–45 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool slightly in the pan before releasing. Dust with powdered sugar before serving, if desired.