Preheat the oven to 350°F.
Remove the dough from the refrigerator and allow it to rest for 5 minutes. Roll out the dough on a floured surface until it reaches a diameter of approximately 14 inches.
Gently place the rolled-out dough into a 9-inch deep-dish pie dish, creating decorative edges as desired.
Prepare a large piece of foil by applying nonstick cooking spray, then lay it over the dough in the pie dish with the greasy side down, ensuring it covers the edges.
Fill the center of the foil with pie weights or dry beans. Bake for 35 minutes.
Remove from the oven and lift out the foil along with the pie weights. Let the crust cool completely before proceeding to the filling.
For the filling, start by combining cornstarch and water in a medium-sized bowl, creating a slurry. Whisk in cream, egg yolks, whole egg, vanilla, and cinnamon. Set this mixture aside.
Warm the milk in a saucepan, bringing it to a gentle simmer, then reduce the heat to low to keep the milk warm.
In another clean saucepan over medium heat, melt the butter, brown sugar, and salt. Once melted, allow the mixture to come to a boil and cook while stirring constantly for 2 minutes.
Remove the pan from the heat and gradually pour in the warm milk, stirring continuously to prevent overflowing.
Slowly whisk in the cream and egg mixture into the saucepan with the brown sugar mixture.
Return the saucepan to the stove and bring it to a boil over medium-low heat, stirring constantly with a silicone or rubber spatula until the mixture begins to thicken. If any lumps form, don't worry; they will be smoothed out in the next step.
Remove the saucepan from the heat, add the butterscotch chips, and whisk until they are melted and the mixture is smooth.
Pour the filling into the cooled pastry crust and allow it to cool on a wire rack.
Once cooled, transfer the pie to the refrigerator and let it chill until it becomes firm, at least 6 hours or overnight.