Lightly spoon flour into a dry measuring cup; level with a knife.
Combine flour, sugar, and salt in a 3- quart saucepan. Combine egg yolks and milk; stir with a whisk. Gradually add egg mixture to dry ingredients, stirring well. Add 2 tablespoons butter. Cook over medium heat until thick and bubbly (about 10 minutes), stirring constantly. Remove from heat; add remaining 1 tablespoon butter and vanilla, stirring until butter melts.
Place 12 vanilla wafers in bottom of an 8-inch square baking dish. Arrange one-third of banana over cookies. Spoon one-third of pudding mixture over banana; repeat procedure with remaining cookies, banana, and pudding, ending with pudding. Spoon whipped topping over pudding, and spread evenly. Cover and chill until ready to serve.