Heat oven to 375 degrees F, arrange rack in upper third, and place a baking sheet on rack while oven heats.
Peel 1 banana and place in a blender with milk, egg yolks, cornstarch, sugar, vanilla, and salt and process until smooth. Pour into a small saucepan, bring to a simmer over medium heat and cook, stirring constantly until mixture bubbles and is thick, about 7 to 8 minutes. Remove from heat and stir in butter, a few pieces at a time, until melted. Set aside to cool slightly.
Pour in filling into the pie shell and evenly smooth with a spatula. Slice remaining 3 bananas into 1/2-inch pieces and arrange on top of custard. Smooth whipped cream over top, loosely cover in plastic, and set in refrigerator until cool and set, at least 3 hours.
Place very clean glass or metal bowl and metal whisk in freezer just until cold, about 5 minutes.
When everything is cold, place cream in bowl and begin to whisk until it froths up and starts to thicken, about 1 minute. Whisk vigorously until soft peaks form (the cream will hold a point when the whisk is lifted but will fall back into the bowl almost immediately), about 1 minute.
Add the liqueur and whisk until stiff peaks just form (the cream stays put on the whisk when it is lifted from the bowl), about 1 minute. Store covered in refrigerator until ready to use.