Preheat oven to 350.
Grease and flour a 9 X 13 pan.
In a large bowl, beat eggs and then add sugar and vanilla and beat until light in color, about 4 minutes.
Stir in flour, salt, and baking powder until just incorporated.
In a medium saucepan, bring milk and butter to boil.
Stir into flour mixture (don't beat, just stir in)
Pour batter into pan and bake for 30 minutes.
While the cake is baking, prepare the icing.
Remove cake from oven and turn off oven.
Then turn on broiler.