Meanwhile, in an electric mixer fitted with the whisk attachment, combine eggs and sugar on medium-high speed for 5 minutes. In a medium bowl, sift together flour, baking powder, and salt.
In a small saucepan over low heat, melt the butter. Stir in milk and vanilla and continue to heat until small bubbles form around the outside of the pan and the mixture is very hot but not boiling. Reduce heat to low.
Preheat the oven to 325°F. Adjust an oven rack to the middle position. Grease and flour a 12-cup tube pan or Bundt cake pan.