Heat oven to 350F, grease and flour two 9-inch round cake pans.
Whisk flour, baking powder and salt in a bowl.
Beat butter and sugar until light and fluffy, about 3 minutes, add eggs one at a time.
Beat in vanilla, then add the flour mixture and milk alternately in three additions, ending with flour, mix just until smooth.
Divide batter between the pans, bake 28 to 32 minutes until a toothpick comes out clean, cool in the pans 10 minutes, then turn onto a rack to cool completely, about 1 hour.
Beat butter for the buttercream 2 minutes until pale, add powdered sugar 1 cup at a time, then cream and vanilla, beat 3 minutes until fluffy and spreadable.
Set one cake layer flat side up on a board or platter, this becomes the face.
From the second layer, cut two ear shapes and one small bow tie shape with a sharp knife, following a paper template.
Arrange the ears above the face layer and the bow tie below it, leaving a small gap to suggest a neck.
Spread a thin crumb coat of buttercream over the whole shape, chill 15 minutes until firm to the touch.
Frost the whole bunny with the remaining buttercream, then press shredded coconut gently into the icing for a furry texture.
Add candy eyes, a pink nose and three licorice whiskers on each cheek, chill 20 minutes before slicing.
Good to Know
Bake the layers up to a month ahead and freeze wrapped; thaw overnight and do the cutting and frosting the day before serving.