Melt 2 tablespoons butter in skillet, add 1/4 cup coconut; stir constantly over low heat until golden brown. Spread coconut on absorbent paper to cool.
Cream 2 tablespoons butter with cream cheese. Add milk and sugar alternately, beating well. Add vanilla; stir in 1 3/4 cups of the coconut.
Spread on top and sides of cake layers. Sprinkle with remaining coconut.
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