Preheat the oven to 350 degrees F (175 degrees C). Grease the sides and bottom of a 10-inch deep-dish pie pan.
Make the crust: Whisk flour, pudding mix, baking powder, and salt together in a bowl. Add milk, butter, and egg; beat with an electric mixer for 2 minutes. Pour into the prepared pie pan.
Make the filling: Drain peaches, reserving 3 tablespoons syrup. Mix 1 tablespoon sugar and cinnamon together in a small bowl.
Beat cream cheese in another small bowl until fluffy. Add 1/2 cup sugar and reserved syrup; beat for 2 minutes.
Arrange sliced peaches over crust mixture. Spoon cream cheese mixture over peaches to within 1 inch of the pan edge, then sprinkle cinnamon sugar over top.
Bake in the preheated oven until golden brown, 30 to 35 minutes. Let cool for 20 minutes, then chill for at least 2 hours before serving.