In a food processor, combine all-purpose flour, ground cinnamon, granulated sugar, and salt. Pulse in cold butter and shortening until mixture resembles coarse crumbs. Gradually add ice-cold water, blending until the dough holds together. Gather dough into a ball, flatten into a disk, wrap in plastic, and chill in the refrigerator for 1 hour.

Roll the chilled dough on a floured surface to a 12-inch circle and fit into a 9-inch pie dish. Freeze crust for 30 minutes while preheating oven to 350°F (175°C). Line the crust with parchment and fill with pie weights; bake for 30 minutes. Remove weights and parchment, then bake for an additional 15 minutes until golden. Let cool completely.

In a small bowl, mix cornstarch with water to create a slurry. In a saucepan over medium heat, warm whole milk until steaming but not boiling. In a separate saucepan, melt butter, stir in brown sugar and salt, bringing to a gentle boil. Slowly add the warm milk while stirring continuously.

Whisk heavy cream, egg yolks, and whole egg into the cornstarch slurry until smooth. Gradually add this mixture into the saucepan while stirring consistently. Cook filling over medium heat for 5-7 minutes until it thickens and bubbles gently.

Once the filling has thickened, remove from heat and stir in butterscotch chips until fully melted. Pour the filling into the cooled crust, smoothing the top with a spatula. Cover with plastic wrap and chill in the refrigerator for at least 6 hours, ideally overnight.