Preheat oven to 375 degrees F. Grease and flour a bundt pan. In a small saucepan. melt the butter and the milk together. Do not boil. Set aside to cool for a a bit.
In a mixing bowl, beat the eggs and the sugar until thickened. Add the flour and baking powder. Now add you vanilla and mix well. Pour in hot milk/butter a little at a time while continuing to mix. Batter will be somewhat thin. Now pour the cake batter into the prepared bundt pan and bake for 30 minutes. Cool for 10 minutes and then invert on serving plate.