In a large bowl, use an electric mixer to combine the butter and sugar until well-mixed. Beat in the eggs, and then the milk, cream, flour, vanilla, salt, and nutmeg. Stir in the coconut flakes.
Pour the coconut mixture into the raw pie crust.
Bake until a knife inserted in the center comes out clean, about 50 to 60 minutes. Check the pie at the 45 minute mark (and every 5 minutes after) and if the crust is getting too dark, put a pie crust shield or foil on it to prevent it from over-browning.
Before slicing, cool the pie to room temperature and then refrigerate to chill, about 2 to 4 hours.
If desired, serve the pie topped with whipped cream or Cool Whip and a sprinkle of toasted coconut flakes.
Notes
If using store-bought pie crust, make sure to thaw it to room temperature before using.
For a more intense coconut flavor, add 1/4 to 1/2 teaspoon coconut extract at the same time that you add the vanilla extract.