Start by preheating your oven to 325°F (163°C). Line the bottom of your springform pan with parchment paper. Blend the Nilla Wafers into fine crumbs, mix with sugar and melted butter, then press firmly into the pan. Bake for 10 minutes and let cool slightly.
Beat the cream cheese until smooth, then mix in mashed bananas and sour cream. Add sugar, dry pudding mix, and vanilla, combining gently. Lightly beat eggs separately, then fold them in carefully to prevent cracking.
Wrap your pan in foil and place it in a large roasting pan with boiling water for a water bath. Pour in the filling, smooth the top, and bake until edges are set and center slightly wobbly. Let it cool in the oven with the door cracked for one hour, then transfer to a cooling rack. Chill in the refrigerator for at least 5 hours.