You can use homemade pound cake for this recipe, but I have listed store bought for ease of preparation. This recipe comes from Mrs. Wilkes' Dining Room in Savannah, Georgia. Prep and Cook time does not include the 6 hours of chilling time!
Whisk together 4 cups half-and-half, 4 egg yolks, 1 1/2 cup sugar, 1/4 cup cornstarch, and 1/4 tsp salt in a saucepan over medium-low heat; cook, whisking constantly, 13 to 15 minutes or until thickened. Remove from heat; stir in 3 tbsp butter and 2 tsp vanilla until butter melts.
Layer half of pound cake cubes, half of bananas, and half of pudding mixture in 1 3-qt round baking dish. Repeat layers. Cover pudding, and chill for 6 hours.
Remove pudding mixture from the refrigerator. Preheat oven to 375 degrees.
Combine 1/4 cup sugar and 1/8 tsp salt.
Beat 4 egg whites and 1/4 tsp vanilla at high speed with an electric mixer until foamy. Add sugar mixture, 1 tbsp at a time, and beat 2 to 3 minutes or until stiff peaks form and sugar dissolves.
Spread meringue over pudding.
Bake at 375 degrees for 15 minutes or until golden brown.