Step 1: Preheat oven to 325°F (165°C). Grease a 9x13-inch baking pan.
Step 2: In a medium bowl, combine graham cracker crumbs, 1/3 cup sugar, and melted butter. Press mixture firmly into the bottom of the prepared pan to form the crust.
Step 3: In a large mixing bowl, beat cream cheese until smooth and creamy. Gradually add 1 cup sugar and vanilla extract, mixing until combined.
Step 4: Add eggs one at a time, beating well after each addition. Be careful not to overmix.
Step 5: Blend in sour cream and banana pudding mix until smooth and fully incorporated.
Step 6: Pour half of the cream cheese mixture over the crust. Arrange a layer of banana slices evenly over the filling.
Step 7: Pour remaining cream cheese mixture over the bananas, spreading evenly to cover.
Step 8: Bake for 50-60 minutes, or until the center is set (it may have a slight jiggle) and the edges are lightly browned.
Step 9: Remove from oven and allow to cool completely on a wire rack at room temperature. Once cooled, refrigerate for at least 4 hours, or preferably overnight, before serving.
Step 10: Top with fresh whipped cream and extra banana slices (if desired) before slicing into squares and serving. Enjoy!