Combine the sweetener, coconut flour/xanthan gum, and salt in a large saucepan. Slowly add in the cream.
Meanwhile, separate the 4 egg yolks and 4 egg whites. Set the whites aside for use later. Beat the yolks slightly.
Cook over medium heat, stirring constantly until the mixture becomes thick and bubbly. Reduce heat and cook 2 more minutes.
Remove the pan from heat. Spoon some of the hot pudding mixture into the egg yolks and mix in order to temper them. Pour the egg yolks into the saucepan and mix it in well.
Place pan back on the heat and cook 2 more minutes. Remove from heat.
Stir in butter and vanilla until the butter is completely melted.
Set aside. If you need to, place a piece of plastic wrap on the surface of the hot pudding to prevent a skin forming (for instance, if you make the pudding ahead of time).
Peel the bananas and slice them into the bottom of the pie crust. You can put in as many as you want, but you should have a good thick layer.
Pour the pudding on top of the bananas until it almost fills up the pie crust.