Preheat oven to 350 degrees.
Sift first 6 ingredients together in large bowl.
Add eggs, coffee, milk, vegetable oil and the 2 teaspoons vanilla extract; blend until smooth.
Pour thin batter into a greased 13 x 9-inch baking pan.
Bake for 35 minutes.
Meanwhile, cream butter until soft and sir in confectioners’ sugar, the 1/8 teaspoon salt, the 3 tablespoons milk, and the 1 teaspoon vanilla extract.
Beat until smooth and creamy adding more milk, if necessary.
Spread over warm cake.