In a large bowl, combine peaches with sugar, corn starch, cinnamon and lemon juice. Stir until mixed and transfer into a greased 9x13" pan.
Dot the 3 tablespoons of butter over the top of the peaches evenly.
In a medium-sized bowl combine the snickerdoodle cookie mix (remove and set cinnamon sugar packet aside for later) with the butter and egg. Stir until smooth and combined.
With your hands, form golfball-size balls of dough and press into ¼ inch thick flat disks. Layer dough disks over the peaches until all dough is used and peaches are covered.
Open cinnamon sugar packet and sprinkle over the top of the cookie dough and peaches evenly.
Bake for 30-35 minutes or until the cookies are golden brown and peach layer is bubbling up on the sides.
Cool 10-15 minutes before serving. Serve warm with vanilla ice cream.