Grease a 10-inch round cake pan and dust with unsweetened cocoa powder.
Stir cake mix, 1 1/4 cup water, vegetable oil, and eggs in a large bowl until moistened. Beat with an electric mixer on medium speed until batter is smooth, 2 minutes.
Pour batter into the prepared cake pan.
Bake in preheated oven until the cake top springs back when lightly pressed and a toothpick inserted into the middle of the cake comes out clean, 30 to 35 minutes.
Place a stainless steel bowl and beaters in refrigerator until chilled, at least 20 minutes.
Cool the cake in the pan on a wire rack for 15 minutes before removing to finish cooling completely.
Place unsweetened baking chocolate into a microwave-safe bowl and heat in microwave on high power until chocolate is slightly warmed, about 1 minute. Continue to heat chocolate in 20-second intervals, stirring after each interval, until chocolate is melted and free of lumps.
Stir melted chocolate with sweetened condensed milk in a large bowl until thoroughly combined; whisk in 1/4 cup water and instant chocolate pudding mix until thickened and smooth, about 1 minute. Cover bowl and chill pudding mixture until cold, at least 30 minutes.
Whip cream in the chilled stainless steel bowl with chilled beaters until the cream holds stiff peaks, about 2 minutes. If necessary, use a cloth to touch the steel bowl to avoid warming the bowl.
Remove chocolate pudding mixture from refrigerator and stir until smooth; gently fold whipped cream into pudding mixture to make a fluffy chocolate frosting.
To assemble the cake, cut the cake into 2 equal halves and place the halves together on a cake serving platter with the cut sides down, and rounded sides up. If needed, glue the two cake halves together with a smear of frosting.
Cut a small wedge out of the edge of the cake halves about 1/3 of the way up to form a head.
Attach the cut-out wedge with toothpicks to the bottom of the cake opposite the head to make a tail.
Generously frost the cake with the chocolate cream frosting.
Sprinkle the whole cake with grated chocolate for fur.
Place jelly beans on front of head to make eyes and nose.
Cut 2 large ear shapes from brown construction paper.
Cut 2 smaller ear shapes from pink construction paper for the insides of the ears. Fold together to make the ears and insert into top of the head.
