In a medium saucepan, combine the 3 cups of whole milk and the 14.6-ounce box of cook & serve vanilla pudding mix. Whisk the mixture over medium heat until it begins to thicken and bubble, stirring constantly. This should take about 5-7 minutes. Once thickened, remove from heat and stir in the 1 teaspoon of vanilla extract and 1 cup of the coconut flakes. Set aside to cool.
In a large mixing bowl, pour the 2 cups of heavy cream and add the 2 tablespoons of sugar. Using an electric mixer, whip on medium-high speed until soft peaks form. Be careful not to over-whip; you want a light and fluffy consistency.
Once the pudding has cooled, gently fold in the remaining 1 cup of coconut flakes into the pudding mixture. Then, fold in half of the whipped cream until just combined. This will create a light and airy filling for your pie.
Place one of the baked pie shells on a serving platter. Pour the coconut pudding mixture into the shell, smoothing it out evenly. Top with the remaining whipped cream, spreading it into an even layer.
Cover the pie with plastic wrap and refrigerate for at least 4 hours, or overnight if you have the time. This allows the flavors to meld and the pie to set properly. Serve chilled, garnished with extra coconut flakes if desired.