Stir together sugar, flour, cocoa, baking powder, baking soda and salt in large bowl. Add eggs, milk, oil and vanilla; beat on medium speed of mixer 2 minutes. Stir in boiling water (batter will be thin).
Line muffin cups (2-1/2 inches in diameter) with paper bake cups. Heat oven to 350°F. Fill cups 2/3 full with batter. Bake 22 to 25 minutes. Cool completely.
Make Frosting:
In large bowl, beat 1/2 cup shortening and 1/2 cup butter with electric mixer until light and fluffy. Beat in 1 teaspoon vanilla extract.
Gradually add 4 cups sifted powdered sugar, one cup at a time, beating well on medium speed. Scrape sides and bottom of bowl often. When all sugar has been mixed in, icing will appear dry.
Gradually add 2 tablespoons of milk; beat at medium speed until light and fluffy.