First, preheat the oven to 356 °F (180 °C).
Then, in the large bowl of a stand mixer fitted with the wire whip attachment, beat the eggs on high speed for about 5 minutes, or until the mixture becomes thick, doubles in volume, and turns a pale yellow color.
Next, gradually add the sugar while continuing to beat. Continue mixing for 2 to 3 more minutes, or until the mixture is light and fluffy.
After that, add the vanilla extract and beat briefly to combine.
In a separate small bowl, combine the flour with the baking powder.
Then, slowly add this dry mixture to the batter while beating on low speed, just until smooth and fully incorporated.
Meanwhile, in a small saucepan, heat the milk together with the butter over low heat until the butter is fully melted, and the mixture is hot, but not boiling.
After that, gradually pour the warm milk and butter mixture into the batter, mixing on low speed until everything is just combined—do not overmix.
Next, pour the batter into a greased 10-inch springform pan and spread it evenly.
Then, place the pan in the oven and bake at 356 °F (180 °C) for 35 to 40 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Finally, remove the cake from the oven and allow it to cool completely before slicing and serving.
