Preheat your oven to 350°F (175°C) and grease a 9-inch round cake pan. Line the bottom with parchment paper for easier removal.

In a large mixing bowl, whisk together the Greek yogurt and granulated sugar until smooth.

Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

In a separate bowl, combine the baking powder, salt, and flour. Gradually add this dry mixture to the yogurt mixture, stirring until just combined.

Gently fold in the melted butter until fully incorporated. Be careful not to overmix.

Pour the batter into the prepared cake pan and smooth the top with a spatula.

Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out clean.

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

Once cooled, dust the top with powdered sugar if desired before serving.