Preheat the oven to 350°F (175°C). Grease a 9×13-inch baking pan with butter or a non-stick cooking spray to ensure easy removal of the cake after baking.

In a medium-sized mixing bowl, combine the all-purpose flour and baking powder. Whisk thoroughly to ensure the baking powder is evenly distributed within the flour. Set aside.

Using a stand mixer or a hand mixer on medium-high speed, whisk the eggs for approximately 3 to 5 minutes until they become pale, thick, and fluffy. This process is essential for achieving a light, airy texture in the final cake.

In a small saucepan, combine the milk and unsalted butter. Warm the mixture over medium-low heat until the butter melts completely and small bubbles appear around the edges. Avoid boiling.

Gradually add the granulated sugar and vanilla extract to the whipped eggs, continuing to beat the mixture on medium-high speed. The result should be a smooth and glossy mixture.

Add the flour mixture to the egg and sugar mixture in increments, mixing at a medium speed until fully incorporated. Be cautious not to overmix.

Reduce the mixer speed to low. Carefully and slowly pour the hot milk and butter mixture into the batter. Continue mixing until just combined. The batter should be smooth and slightly thin.

Pour the prepared batter into the greased baking pan and transfer it to the preheated oven. Bake for approximately 30 to 35 minutes, or until a toothpick inserted into the center comes out clean.

Allow the cake to cool in the pan for about 10 to 15 minutes. Then, carefully transfer it to a wire rack to cool completely before serving. This cake pairs wonderfully with whipped cream, fresh berries, or a drizzle of chocolate sauce.