Add water to saucepan. Whisk in flour until smooth. Add sugar and mix well. Add eggs, one at a time, mixing well after each one. Slowly stir in milk, mixing well.
Place pan on low heat. Cook, stirring constantly, until mixture is thickened to the consistency of a thick gravy, approximately 20 minutes. The mixture will start to steam and produce bubbles, but you don't want a full boil.
Remove from heat and stir in vanilla. Cool thoroughly. Fold in sour cream and mix well.
Layer wafers, bananas, and pudding in a glass serving bowl, such as a trifle bowl. Thoroughly chill. Serve with whipped cream.