Line bottom of 3-quart glass serving bowl with vanilla wafers in single layer. Prepare instant pudding mix according to package directions, using milk and 1/2 cup cream. Beat in 2 teaspoons vanilla.
Layer one-fourth of banana slices over wafers. Spoon on one-fourth of pudding, spreading evenly. Top with a layer of vanilla wafers. Repeat layering, ending with pudding.
Beat together remaining 1-1/2 cups cream, remaining 1 teaspoon vanilla and the sugar in small bowl until soft peaks form. Spoon on top, spreading level. Loosely cover; refrigerate overnight.