Directions Start with a 350°F oven. Mix sugar, flour, and salt in a pot. Add milk slowly. Stir frequently over medium heat until mixture boils and thickens. Cook and stir for 2 more minutes, then remove from heat.
Whisk egg yolks in a medium basin with a little hot milk mixture until creamy, then slowly add to saucepan. Stir continuously over medium-low heat until mixture coats the back of a spoon, about 2 minutes more. Remove from heat and add butter and vanilla.
Pour pudding mixture over sliced bananas in pastry shell. Bake 12–15 minutes in preheated oven until filling settles. Let pie cool fully on a wire rack, then refrigerate for at least 1 hour before serving.