Preheat your oven to 350°F (175°C). Grease and line an 8-inch round cake pan with parchment paper.
Prepare Dry Ingredients:
In a medium bowl, sift together the flour, baking powder, and salt. Set aside.
Beat Eggs and Sugar:
In a large bowl, use an electric mixer on high speed to beat the eggs and sugar together until the mixture is thick, pale, and tripled in volume, about 5 minutes.
Combine Dry Ingredients:
Gently fold the sifted dry ingredients into the egg mixture in batches, being careful not to deflate the batter.
Add Wet Ingredients:
In a small bowl, mix the melted butter and milk together, then add the vanilla extract.
Gently fold this mixture into the batter until just combined.
Bake the Cake:
Pour the batter into the prepared cake pan, gently tapping the pan on the counter to release any air bubbles.
Bake in the preheated oven for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Cool and Serve:
Let the cake cool in the pan for 10 minutes, then transfer it to a wire rack to cool completely.
Serve the génoise as is, or with your favorite toppings like fresh fruits and whipped cream.