Begin by browning ½ cup of butter in a saucepan over medium heat until it turns golden and releases a nutty aroma. Meanwhile, combine 1 ½ cups crushed vanilla wafers and ¼ cup sugar in a mixing bowl. Pour the melted butter into the wafer mixture, stirring until all crumbs are evenly coated. Firmly press the mixture into the bottom of a 9-inch springform pan to form a solid crust.

Preheat your oven to 350°F (175°C). Place the crust in the oven and bake it for 10 minutes, or until it appears golden and fragrant. Allow it to cool completely at room temperature before adding the filling.

In a large mixing bowl, beat 16 ounces of softened cream cheese and ¾ cup of sugar together using an electric mixer on medium speed until smooth and creamy, about 2-3 minutes. Add in 3 large eggs, one at a time, mixing well after each addition.

Fold in 2 mashed overripe bananas and 1 teaspoon of vanilla extract into the cream cheese mixture until evenly distributed, ensuring no lumps remain.

Pour the banana-infused filling into the cooled crust, spreading it evenly. Bake for approximately 55-65 minutes until the edges are firm and the center has a slight jiggle.

Once baked, let the cheesecake cool to room temperature, then cover and refrigerate for at least 4 hours or overnight.

Combine 1 box of instant pudding mix with 2 cups of milk and whisk until smooth. Spread over the chilled cheesecake and allow to set for at least 30 minutes in the refrigerator.