Preheat oven to 325°F (160°C).

In a medium bowl, combine graham cracker crumbs and melted butter. Press the mixture into the bottom of a 9-inch springform pan. Bake for 10 minutes, then let cool.

In a large bowl, beat the cream cheese and sugar until smooth. Add peanut butter and vanilla extract, mixing until well combined. Add eggs one at a time, beating after each addition. Stir in the heavy cream.

Pour the filling over the cooled crust. Bake for 50-60 minutes, or until the center is set. Let cool to room temperature, then refrigerate for at least 4 hours or overnight.

In a medium saucepan over medium heat, melt the sugar, stirring constantly until it turns a golden brown color. Add the butter, stirring until melted. Slowly add the heavy cream, stirring until smooth. Remove from heat and let cool slightly.

Pour the caramel over the chilled cheesecake, spreading evenly. Refrigerate for 30 minutes.

Arrange banana slices on top of the cheesecake. Sprinkle with chopped peanuts. Drizzle with caramel sauce before serving.