Resift flour with sugar, cocoa, baking powder and soda into bowl. Gradually stir in mayonnaise. Stir in water and 1 1/2 teaspoons vanilla. Fill 2 dozen greased or paper-lined muffin pans 1/2 full with batter. Bake at 350F 25 to 30 minutes. Cool in pans 5 minutes. Remove from pans and cool on rack.
2. Meanwhile, to make frosting, melt butter and chocolate in top of double boiler over hot water. Sift powdered sugar with salt. Add chocolate mixture and blend. Beat in enough milk to make spreadable. Beat in 1/2 teaspoon vanilla. Use to frost cupcakes. Garnish tops with nuts, if desired.
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