For the filling, whisk together the cornstarch and water until smooth. Mix in the cream, egg yolks, whole egg, vanilla, cinnamon, and nutmeg, and set aside while preparing the butter-sugar mixture.
In a saucepan over medium heat, melt the butter with light brown sugar and salt, stirring constantly for a few minutes until it bubbles gently. Slowly add the warm milk, stirring continuously to keep the mixture smooth and prevent it from spilling over.
Gradually stir the cream-and-egg mixture into the butter-sugar mixture and cook over medium-low heat, stirring constantly, until it thickens into a silky, luscious custard. A silicone spatula works best here to scrape the bottom and prevent curdling.
Take the pan off the heat and stir in the butterscotch chips until completely melted and smooth. Take a deep breath, the rich caramel aroma is irresistible.
Pour the filling into the cooled crust and let it sit on the counter for a few minutes. Then transfer the pie to the fridge and chill until firm, about 8 hours or overnight, so it slices perfectly every time.