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Step 1
Adjust oven rack to middle position and preheat oven to 350 degrees. Grease an 8-inch round cake pan and line with parchment paper. Grease parchment paper and flour pan.
Step 2
In a small bowl, mix milk, vanilla, and egg whites together. Set aside. In a standing mixer fitted with a paddle attachment, mix together flour, sugar, baking powder, and salt on low speed until combined. Add butter, one piece at a time, and mix until only pea-sized pieces remain, about 1 minute.
Step 3
To the mixing bowl, add half of the milk mixture and increase speed to medium-high. Beat until the mixture is light and fluffy, about 30 seconds. Add remaining milk mixture and beat on medium-low speed until incorporated, about 15 seconds. Do not over mix. Give the batter a final stir by hand.
Step 4
Pour batter into prepared pan and smooth the top using a rubber spatula. Bake until top is light golden and a wooden toothpick inserted into the center of the cake comes out clean, about 20 to 25 minutes. Rotate pan halfway through to ensure even baking.
Step 5
Cool cake in pan on a wire rack for 10 minutes. Remove cake from pan and allow to cool completely before frosting, about 2 hours.
Step 6
In a standing mixer fit with the paddle attachment on medium-high speed, cream butter until pale and fluffy, about 3 minutes.
Step 7
Reduce mixer speed to low. Add 2 cups powdered sugar, cream, vanilla, and salt (if using). Continue mixing 2 to 3 minutes longer. If the frosting seems too soft, add the remaining powdered sugar 1 tablespoon at a time. Cover and refrigerate the frosting until ready for use.
Step 8
Cut cake in half. Using prepared buttercream frosting, frost the top of one half of the layers. Place other layer on top and stand cake on serving platter to form the bunny cake's body. Cut a notch about 1/3 of the way up on one side to form the bunny cake's neck and head. Using frosting, attach removed pieces to opposite end of the notch to form the bunny's tail.
Step 9
Frost outside of the cake with remaining buttercream frosting, rounding out the sides of the body. Sprinkle the bunny with coconut flakes, gently pressing in coconut so it sticks to the sides.
Step 10
Using construction paper or another thick type of paper, cut 2 4-inch by 1 3/4-inch bunny ears (use watercolors to paint them if desired). Cover ends of ears with plastic food wrap and insert in the top of the notch on the cake. Insert jelly bean for bunny's nose.