Preheat oven to 400◦. Lightly grease a 12 x 17-inch rimmed baking sheet with non-stick cooking spray.
Whisk eggs in a large bowl.
Bring water and butter to a boil in a medium saucepan over medium-high heat. Stir in flour and salt; continue cooking and stirring until the mixture forms a stiff ball.
Add flour mixture to eggs and whisk quickly and vigorously until completely incorporated and smooth.
Drop batter by large spoonfuls (about 1/4 cup) onto prepared baking sheet. Bake until lightly browned, about 35 minutes. Do not open the oven during the first 30 minutes of baking!
Transfer cream puffs to wire racks and cool completely.
Prepare pudding mix according to package directions, using 2 cups milk.
Using an electic mixer, beat cream cheese until smooth. Blend in pudding.
Carefully cut cream puffs in half. Spoon pudding mixture over bottoms then cover with tops.
Melt chocolate with remaining 2 tablespoons milk in a small non-stick pan over medium-low heat, stirring occasionally. Drizzle melted chocolate over cream puffs.