Preheat the oven to 350 F and prepare a 9 inch round cake pan by lightly greasing.
In a mixing bowl, combine sifted flour, baking powder, and salt. In a small sauce pan over very low heat, combine milk and butter.
In a separate bowl, beat egg and sugar on high until thickened and lighter in color, about 5 minutes. Slowly whisk in flour mix until just incorporated.
Bring the milk and butter to a boil, then pour into the batter. Mix just until smooth, then add the vanilla. Pour into prepared baking dish and bake until it passes the toothpick test and the edges are pulling away from the side of the pan, about 35 to 40 minutes.
Remove from oven and let cool in pan for 10 minutes, then transfer to a wire rack to cool completely.