1Preheat oven to 350 degrees F (175 degrees C). Grease and flour two 9-inch round cake pans. Sift together the flour, baking soda, and cocoa. Set aside.
2Combine the coffee and coffee liqueur. Set aside. In a large bowl, cream together the shortening and brown sugar until light and fluffy. Beat in the egg yolks one at a time. Beat in the flour mixture alternately with the coffee and coffee liqueur, mixing just until incorporated. In a separate bowl, beat egg whites until soft peaks form, add 1/4 cup sugar, then continue beating until whites form stiff peaks. Gently fold egg whites into the coffee mixture.
3Pour batter into prepared pans. Bake in the preheated oven for 30 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow to cool 10 minutes in pans, then turn out on wire racks to cool completely before frosting.
4For the coffee frosting: In a medium bowl, cream butter until fluffy. Beat in confectioners' sugar and cocoa. Mix in coffee liqueur and hot coffee. Beat frosting until it thickens to spreading consistency.