In medium bowl, whisk together flour, baking powder, and salt.
In small bowl, mix together milk and vanilla.
Place sugar and eggs in mixer bowl. Beat together on medium-high speed until light and slightly thickened, approx. 3 minutes.
Reduce speed to medium.
While mixer is running, gradually add melted butter, then milk/vanilla mixture, pouring into side of bowl.
Mix until batter is smooth and has sheen.
Reduce speed to low.
While mixer is running, gradually add dry ingredients.
Just before flour mixture is fully incorporated, stop mixer and stir with spatula to finish.
Scrape batter into springform pan.
Place filled pan on baking sheet. (This will make it easier to get the cake in and out of the oven.)