FOR THE CAKE:
Sponge cakes are a late-18th-/early-19th-century creation, achieving a light texture through beating egg yolks and sugar together until they turn pale and lemon-colored. This recipe also uses beaten egg whites and baking powder, so it achieves beautifully lofty heights, as the name implies. The mild coffee flavor is enhanced by the satiny icing.
Preheat oven to 350°. In a small bowl, dissolve instant coffee in boiling water, and set aside to cool.
In a medium bowl, sift together flour, baking powder, and salt.
In a large bowl, beat egg whites with cream of tartar until soft peaks form. Add ½ cup of the sugar to the egg whites a little at a time, and continue beating until firm, glossy peaks form. Set whites aside.
In another large mixing bowl, beat egg yolks until smooth, then gradually add remaining 1-½ cups sugar and vanilla. Beat at high speed until thick and lemon-colored (about 5 minutes).
Add the dry ingredients alternately with the cooled coffee to the egg yolk mixture, beginning and ending with dry ingredients. Blend thoroughly. Fold in nuts. Lightly fold in the beaten egg whites until evenly blended.
Pour into an ungreased 10-inch tube pan and bake until fully cooked, 60 to 70 minutes.
Immediately invert the pan and set the hole in the center atop a heatproof funnel or bottle to let it cool upside-down (this protects the cake from sinking). Cool completely, about 45 minutes.
FOR THE ICING:
Meanwhile, make the icing: Cream butter. Add confectioners' sugar, instant coffee, and salt and mix well. Gradually add milk until icing is of spreading consistency. Frost cake and sprinkle with chopped nuts if desired.