Open the can of peach pie filling and place it in a bowl. Run a knife through the bowl of pie filling to cut the peaches into small, bite-sized chunks.
Place the refrigerated pie crust on a prepared baking sheet. Use a fork to poke small holes in it. Bake it at 400F for 10-12 minutes or until golden brown.
Allow the pie crust to cool completely and use your hands to break it into small pieces.
In a large mixing bowl, whip the heavy cream until stiff peaks form. In another bowl, stir together the sweetened condensed milk, vanilla instant pudding mix, and vanilla extract. Gently fold the whipped cream into the condensed milk mixture until combined.
Gently fold in the crumbled pie crust and the prepared peach pie filling.
Place the no churn peach cobbler ice cream into an air-tight freezer-safe container. Crumble additional pie crust pieces over the top for extra crunch and flavor. Allow it to freeze for at least 4 hours, or overnight for the best texture, before serving.