In the bowl of an electric mixer fitted with the paddle attachment, combine 1 stick butter, 1/2 teaspoon vanilla, and 1 1/2 cups sugar; mix on medium-high speed until pale and fluffy, about 2 minutes. Stir in food coloring to make pale yellow. Transfer to a small bowl; cover.
Put remaining 3 sticks butter in mixing bowl. Beat on medium-high speed until pale and creamy, about 2 minutes. Reduce speed to medium; add cocoa. Mix until smooth. With mixer running, add remaining 3 3/4 cups sugar, 1 cup at a time. Add remaining 1/2 teaspoon vanilla; mix on high speed until incorporated, 10 to 20 seconds more.
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These icings worked well with the cake. The chocolate makes enough to frost the cake, but the yellow icing is overkill. You could easily make half of the yellow icing.
For the chocolate part, you have to double the butter.