Prep. Preheat oven to 325 degrees. Grease and line two 8-inch round cake pans with parchment paper.
Mix dry ingredients. Sift the cake flour, baking powder, salt, and baking soda together through a mesh strainer into a bowl. Set aside.
Beat oil, butter, and sugar. In a stand mixer fitted with the paddle attachment, cream the butter, oil, and sugar on medium speed until light and creamy, about 2 minutes. Add the egg whites and mix on medium until incorporated, 45 to 60 seconds.
Mix wet ingredients. Whisk together the milk, sour cream, vanilla, and almond extract in a small bowl.
Alternate wet and dry into butter mixture. With the mixer on low, alternate adding the flour mixture and milk mixture in three additions of flour and two of milk, beginning and ending with flour. Mix on low until just combined after each addition. Stir the batter once with a rubber spatula.
Bake. Divide the batter evenly between the prepared pans (about 675 grams per pan). Bake for 35 minutes, until deep golden brown and a toothpick inserted in the center comes out clean. Cool in pans on wire racks for 10 to 15 minutes, then invert onto racks to cool completely, about 1 hour.
Make frosting. For the frosting, cream the butter on medium-high for 3 to 4 minutes until light in color. Add powdered sugar in two additions, mixing on low then increasing to medium. Add the extracts and 1 to 2 tablespoons of cream, mix until smooth. Add additional cream a tablespoon at a time until spreadable.
Cut and arrange. Cut the bunny shape from one cake layer: measure 2½ inches from one edge toward the center and cut a curved piece for one ear. Repeat on the opposite side for the second ear, leaving a bowtie shape in the middle. Place the uncut round layer on a serving board. Arrange the ears at the top and bowtie at the bottom.
Decorate. Frost the face and ears with white frosting and cover with coconut. Tint 1½ cups coconut pink by shaking in a bag with a small amount of pink gel. Tint 1 cup of frosting light pink. Frost the bowtie with pink frosting and top with pink coconut. Add pink coconut to the cheeks and inner ears. Place two dark jellybeans for eyes and a pink one for the nose. Decorate the bowtie with jellybeans or preferred Easter candy. Use edible grass, licorice, or gum for whiskers.