Preheat the Oven: Preheat your oven to 350°F (175°C). Grease a round cake pan (8-9 inches) with butter or line it with parchment paper.
Beat the Eggs and Sugar: In a large mixing bowl, whisk the eggs and sugar together until the mixture becomes light and fluffy, about 5-7 minutes.
Combine the Dry Ingredients: In a separate bowl, sift together the flour, baking powder, and salt.
Fold in Dry Ingredients: Gently fold the dry ingredients into the egg mixture using a spatula, and add the lemon zest and vanilla extract.
Pour the Batter into the Pan: Transfer the batter into the prepared cake pan and smooth it out with a spatula.
Bake the Cake: Bake in the preheated oven for about 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Cool the Cake: Let the cake cool in the pan for 10 minutes, then transfer it to a wire rack to cool completely.
Serve: Once the cake has cooled, dust with powdered sugar or top with whipped cream and fresh fruit if desired.