Whisk sugar, cornstarch, and salt in a saucepan. Gradually whisk in milk and egg yolks until smooth, checking that no dry starch remains.
Cook over medium heat, whisking continuously across the base and corners, until the pudding thickens and begins to bubble gently.
Keep whisking for 1 minute once bubbling begins. Remove from heat, stir in butter and vanilla, and cover the surface directly with food-safe wrapping.
Cool the pudding for about 20 minutes, stirring once to release heat. Slice bananas shortly before assembling to reduce browning.
Spread a little pudding in the serving dish. Add half the wafers, half the banana slices, and half the remaining pudding.
Repeat with the rest of the wafers, bananas, and pudding. Cover and refrigerate at least 3 hours, allowing the wafers to soften.
Whip cold cream and powdered sugar to medium-stiff peaks. Spread over the chilled pudding just before serving, keeping the layers beneath undisturbed.
Spoon into bowls with a broad serving spoon. Return unused pudding to the refrigerator promptly, keeping fresh banana slices beneath the pudding where possible.
