To prepare ice cream, place pie dough on a baking sheet lined with parchment paper; lightly coat with cooking spray. Combine 1 tablespoon sugar and cinnamon in a small bowl. Sprinkle sugar mixture evenly over pie dough. Using a knife or pizza cutter, score dough at 1-inch intervals. Bake at 425° for 10 minutes or until browned. Cool completely; break into 1/2-inch pieces.
Place 1/2 cup peaches in a medium bowl, and mash with a fork until almost smooth. Add the remaining 1/2 cup peaches and next 4 ingredients (through dash of salt); stir well. Gently fold in the crumbled piecrust and whipped topping. Scoop the mixture into a freezer-safe container; cover and freeze overnight.
To prepare sauce, combine 1/2 cup sugar, 2 tablespoons water, corn syrup, and dash of salt in a small saucepan over medium heat, stirring just until sugar melts; bring to a boil. Cook 12 minutes or until amber; remove from heat. Drizzle in half-and-half, stirring constantly with a whisk. Add butter and bourbon; whisk until smooth.