PREPARE cake batter, in 2-1/2-qt. ovenproof bowl, as directed on package; scrape side of bowl. Beat cream cheese, egg, vanilla, and granulated sugar until well blended; spoon into center of batter in bowl.
BAKE 1 hour 5 min. or until toothpick inserted in center comes out clean. Cool cake in bowl 10 min. Loosen cake from bowl with knife; invert onto wire rack. Remove bowl. Cool cake completely.
MEANWHILE, beat dry pudding mix, powdered sugar and milk in bowl with whisk 2 min. Stir in COOL WHIP. Refrigerate until ready to use.
PLACE cake on plate; frost with pudding mixture. Cover with coconut. Keep refrigerated.