Preheat oven to 350°. Process cookies and peanuts in a food processor about 1 minute or until finely chopped. Stir together cookie mixture and melted butter. Press crumb mixture on bottom, up sides, and onto lip of a lightly greased 9-inch pie plate.
Bake at 350° for 10 to 12 minutes or until lightly browned. Transfer to a wire rack, and cool completely (about 30 minutes).
Whisk together granulated sugar and cornstarch in a large, heavy saucepan. Whisk together half-and-half and egg yolks in a medium bowl. Gradually whisk half-and-half mixture into sugar mixture, and bring to a boil over medium heat, whisking constantly. Boil, whisking constantly, 1 minute; remove from heat.
Stir butter, peanut butter, and 1 tsp. vanilla into sugar mixture. Place heavy-duty plastic wrap directly on warm custard (to prevent a film from forming), and cool 30 minutes.
Cut bananas into 1/2-inch-thick slices; place in a single layer on bottom of crust, covering bottom completely. Spoon custard mixture over bananas; cover and chill 4 to 48 hours.
Beat cream at high speed with an electric mixer until foamy; gradually add powdered sugar and remaining 1 tsp. vanilla, beating until soft peaks form. Top pie with whipped cream mixture. Serve immediately, or chill up to 4 hours.
Note: We tested with Nabisco Nutter Butter peanut butter sandwich cookies.