Preheat your oven to 350°F (175°C) and prepare a 9-inch round cake pan by greasing it and lining with parchment paper.

In a mixing bowl, whisk together the yogurt, eggs, sugar, butter, and vanilla until smooth.

In a separate bowl, sift together the flour, baking powder, salt, and lemon zest.

Fold the dry ingredients into the wet mixture in batches until just combined.

Pour the batter into the prepared cake pan and smooth the top.

Bake for 25-30 minutes until golden brown and a toothpick comes out clean.

Let the cake cool in the pan for 10 minutes before transferring it to a wire rack.

Dust with powdered sugar before serving.