Preheat oven to 325 degrees F. Line a rimmed baking sheet with foil and place the frozen pie crust (in its pan) on top. The rimmed baking sheet will catch any drips. Prick small holes with the tines of a fork on the bottom and sides of the pie crust; this will help from creating air bubbles. Likewise, you may also fill the pie crust with pie weights to weigh it down during baking. Bake the crust for 10-12 minutes. Remove from the oven but keep the oven on.
While crust bakes, prepare your filling. In a medium saucepan, whisk together the cornstarch and granulated sugar until no clumps remain and mixture is cohesive. Whisk in the melted butter, eggnog, and nutmeg and turn the stove on medium. Cook and stir constantly until mixture thickens and becomes smooth and creamy, about 5-7 minutes. It should look like pudding. Remove from heat and whisk in the vanilla extract.
Pour the filling into the prepared partially-baked pie crust and smooth out the top. Pour the melted butter topping over the pie filling and sprinkle the cinnamon sugar mixture liberally over the top.
Bake for 25 minutes, then turn on the broiler and broil for 1 minute or until topping is golden brown and bubbly (watch it carefully to prevent burning!). Cool the pie completely at room temperature before refrigerating for at least 1 hour to set
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