Preheat your oven to 350°F (175°C). Grease an 8-inch round cake pan with butter or cooking spray, and optionally line the bottom with parchment paper.

In a medium mixing bowl, combine all-purpose flour, baking powder, and salt. Whisk until evenly mixed, and then set aside.

In a large bowl, whisk together eggs, yogurt, granulated sugar, vegetable oil, and vanilla extract until smooth and fluffy. Optionally fold in lemon zest.

Gradually add the dry ingredients into the wet mixture, stirring gently until just combined. A few lumps are fine.

Pour the batter into the prepared cake pan, smoothing the top with a spatula.

Bake in the preheated oven for 30 to 35 minutes, until the top is golden and a toothpick inserted comes out clean.

Let the cake cool in the pan for about 10 minutes. Then transfer to a wire rack to cool completely before serving.