For the pie crust pieces: Preheat oven to 350 degrees. Tear pie crust into ½-inch to 1½-inch pieces. Combine sugar, cinnamon, and fleur de sel in a small bowl. Toss pie dough pieces in sugar mixture then arrange in an even layer on a rimmed baking sheet. Bake for 10 min., tossing every few min. to get an even golden color. Set aside to cool. Store sealed in bag in the refrigerator until ready to prepare ice cream.
For the ice cream: Cream base: Mix cornstarch with ¼ cup of the milk; set slurry aside. In a 4-quart saucepan, whisk remaining milk, cream, sugar, syrup and salt. Bring to a boil over medium-high heat and cook for 4 min. Stir in slurry, return to a boil and cook, stirring, until thickened, about 2 min. Place cream cheese in a bowl and pour in ¼ cup of the hot milk mixture; whisk until smooth. Whisk in remaining hot milk mixture. Remove from heat and stir in vanilla bean paste. Pumpkin layer: Transfer one cup of the cream base to a separate bowl and whisk in pumpkin puree and Pumpkin Pie Spice until smooth.
To finish: Pour each ice cream layer mixture into a separate plastic bag; seal and submerge in a bowl of ice water until chilled. First, process the cream base in an ice cream maker using the manufacturer's instructions. Transfer frozen cream base to a container, cover and set in the freezer. Next, clean out ice cream maker and process the pumpkin layer. Immediately fold the frozen pumpkin layer and prepared pie dough bites into the frozen cream base. Tip: Swirl layers together in several figure 8s, trying not to mix entirely. Transfer to a freezer-safe container, cover and freeze until set. Serve by dragging a preheated ice cream scoop through to the bottom of the container to get a get good mix of the each layer plus the pie crust bites.