For the frosting: Combine the sugar, butter and salt in the bowl of a stand mixer fitted with a paddle attachment (or in a large bowl if using a hand-held electric mixer). Mix on low speed until mostly incorporated. Add the vanilla, increase the speed to medium high and mix until smooth. Adjust the consistency with milk until the frosting is easy to spread.
For the bunny: Spread a thin layer of frosting (about 2/3 cup) on the flat side of one cake layer and top with the flat side of the second cake layer. Measure 5 inches across the top of the cake and cut down through the layers, creating 2 layered pieces that are slightly different sizes.
Place the larger piece of cake cut-side down on a large platter or cake board. If using a rectangular cake board, place the larger piece so that the long edges are parallel with the long edges of the board. This is the body of the bunny. Cut the smaller piece of cake in half crosswise, so you have 2 layered wedges. Place one wedge in front of the body, with one flat side on the board and the other flat side against the body. The curved side will be on top. Take a serrated knife and round off the sharp edges on top of the head. Cut the tip off (the nose) at a 45-degree angle. Reserve all scraps in a bowl.
Separate the layers of the remaining wedge of cake. These will be the back legs. Round the sharp edges of the cake wedges with your knife and add to the scrap bowl. Place one piece on each side of the bunny, with one flat side down and the other flat side facing forward (the round side towards the back of the bunny), about 1 inch from the end of the bunny’s body.
Mix the cake scraps in the bowl with a fork until mashed and then pack into a ball with your hands. Place the ball behind the bunny’s body and adhere with a dab of frosting. This is the bunny’s tail.
Frost the entire bunny, tail and all, using 2 to 3 cups of the frosting, keeping some definition with the bunny parts and frosting more generously around any sharp edges to give a rounded look to the bunny parts. Sprinkle the bunny with the coconut to fully cover. Gently pat to adhere.
Insert the biscotti between the head and body, pressing into the cake to secure them. These are the ears. Place the base of the ears close together at the center of the head and angle them out. Frost the front of each biscotti with some frosting. Then, using the pink decorating icing, frost a smaller strip in the center of each biscotti, going down to where the ears meet the head but not going all the way to the top.
To make the face, press a black jelly bean into each side of the head for the eyes. Cut one of the marshmallows into 3 circles, discard the middle piece and press the 2 end circles, cut-sides in, into the front of the face for the bunny cheeks. Push the white jelly bean halves into the face below the cheeks, round-sides out, for the teeth. Place the pink jelly bean above for the nose.
Unroll the licorice wheel and cut 2 pieces, each about 1 1/2 inches long. For each piece, peel the strips apart halfway down and then cut each separated strip in half lengthwise so you end up with a piece looking a bit like a broom. Repeat with the second piece of licorice. Tuck each piece, with a dab of frosting, behind a marshmallow cheek, with the cut ends facing out for the whiskers.
Cut the second marshmallow in half lengthwise. Make 3 slits in each half, going about halfway through (these are the toes), and place in front of the legs for the bunny’s feet. Adhere the bottom of the feet with frosting if necessary.
Cut 2 1/2 sheets of parchment paper in half. Line the edges of your cake board with these parchment rectangles so that they form a rectangle of open space in the middle. Build your cake on the edges of these pieces of parchment. When you are finished, you can slide them away along with any excess frosting and coconut. Make sure your cakes are completely cooled before you begin to frost and cut them.