In a large bowl, cream butter and sugar until light and fluffy. Beat in egg yolks. Beat in the bananas, sour cream and vanilla. Combine the flour, baking soda and salt; add to the creamed mixture and mix well.
In a small bowl, beat egg whites until stiff peaks form. Fold into batter. Transfer into two greased and floured 9-in. round baking pans. Bake in a preheated 350º oven for 20-25 minutes or until a toothpick inserted near the center comes out clean. Cool for 10 minutes before removing from pans to wire racks to cool completely.
For filling, in a small bowl, whisk milk and pudding mix for 2 minutes. Let sand for 2 minutes or until soft-set. Cover and refrigerate until chilled.
In a small bowl, beat frosting until light and fluffy. Place bananas in a small bowl; toss with lemon juice.
Place one cake layer on a serving plate; spread with 3 Tbsp. frosting. Stir pudding; spread half over the frosting. Top with half of the bananas and the remaining cake layer. Repeat frosting, filling and banana layers. Frost sides and decorate top edge of cake with remaining frosting. Store in the refrigerator.