Preheat oven to 350°F (175°C).
In a medium saucepan, combine milk, cream, and sugar. Heat over medium until steaming (not boiling).
In a bowl, whisk eggs and cornstarch until smooth.
Slowly pour hot milk into eggs while whisking constantly.
Return the mixture to the saucepan and cook on low, stirring until thickened and coats the back of a spoon.
Remove from heat and stir in vanilla, cinnamon, nutmeg, and salt.
Pour custard into the pie crust.
Bake 50–60 minutes, until set but slightly jiggly in the center.
Cool to room temperature, then refrigerate at least 3 hours before serving.