Heat oven to 35 degrees.
Sift flour, sugar, cocoa, baking soda and salt into a 9x13-inch baking pan.
Add water, oil, vinegar and vanilla.
Mix with a large rubber spatula until smooth, taking care to mix ingredients along edges.
Bake until toothpick inserted in center comes out clean, about 4 minutes.
Cool completely on wire rack.
FROSTING: combine butter and shortening in a food processor or mixing bowl. Add sugar and vanilla.
Mix until smooth, about 2 minutes. Slowly drizzle in milk.
Beat 2 minutes in food processor or 7-1 minutes with a mixer, until smooth, satiny and fluffy.
Chill just 2 minutes before frosting.
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