Preheat the oven to 350°F (175°C). Grease a 9-inch cake pan with butter or non-stick spray.
In a large mixing bowl, whisk together the sifted flour and granulated sugar until well combined, creating an even, powdery mixture.
Add the melted butter, eggs, milk, and vanilla extract to the dry ingredients. Using a hand or stand mixer on low speed, beat until the batter is smooth, silky, and evenly combined, about 2-3 minutes.
Pour the batter into the prepared cake pan, spreading it evenly with a spatula. Tap the pan lightly on the counter to release any air bubbles trapped in the mixture.
Bake in the preheated oven for 30-35 minutes, or until the top is golden brown, a toothpick inserted into the center comes out clean, and the edges start to slightly pull away from the sides of the pan.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes. Then, transfer it to a wire rack and let it cool completely before serving, revealing a soft, tender crumb.