Prepare cake mix according to package directions for making two 8-inch round cakes. Transfer pans to wire rack; let cool 5 minutes. Invert cakes onto wire rack and cool completely.
Using a serrated knife, cut a 6-inch circular indentation in top layer, about 3/4-inch deep. Frost entire cake, stacking layers, with vanilla frosting. Use a large serving fork to create a basket-weave design in frosting on side of cake.
In a small bowl, dilute pink icing color with 2 tablespoons water. Stir in coconut to tint, and spread on a baking sheet to dry slightly. Fill indentation in top of cake with tinted coconut. Nestle Marshmallow Peeps in pink "grass" and add malted-milk eggs and jelly beans. For handle, cover a wooden basket handle with two strips of green felt and insert into cake.