Preheat oven to 350º Fahrenheit. Grease and flour a 2 ½ quart oven safe bowl.
In a separate bowl, prepare cake batter according to the package directions.
Pour the batter into the prepared bowl.
In another small bowl, beat the cream cheese, egg and sugar until well blended, scraping the sides of the bowl as needed. Spoon this mixture into the center of the batter in the bowl, leaving about 2” of chocolate batter around the edges.
Bake 65-70 minutes or until toothpick inserted in center comes out clean.
Allow the cake to cool on a wire rack for about an hour, then loosen cake from bowl with knife. (Note…don’t turn out the cake too soon. The cream cheese takes time to cool and set.)
Invert the cake onto a cake plate and remove the bowl to cool completely.
For the frosting, beat dry pudding mix, powdered sugar and milk in medium bowl until smooth. Stir in whipped topping. Refrigerate the frosting until the cake is cool and you are ready to frost the cake.
Once the cake is cool, frost with pudding frosting. Sprinkle coconut all over the cake.