Make the Ice Cream: Whip heavy cream on high speed until stiff peaks form. Refrigerate until ready to use. Mix peanut butter, sweetened condensed milk, and vanilla together with a hand mixer. Fold together peanut butter mixture with whipped cream. Transfer to a sealable container and freeze until hardened, four hours or overnight.
Make the Chocolate Sauce: Place chocolate chips and vegetable oil in a microwaveable bowl. Heat 1 minute, or until chocolate begins to melt. Stir until melted and combined. Stir in roughly chopped peanuts. Place in a jar and let come to room temperature.
Make the Cookies: Preheat oven to 350°. Spray a whoopie pie pan with cooking spray. Cream butter, peanut butter, and brown sugar and white sugar until well combined. Mix in egg and vanilla. Add salt and baking soda and mix well. Add flour and mix until just combined. Stir in chopped peanuts and chocolate chips. Scoop large spoonfuls (about 2 tablespoons) into pan, press to fit. Bake for 8 to 10 minutes, until edges are brown. Centers will still be a little gooey. Remove from oven and cool 10 minutes before removing from pan.
Assemble the Sundaes: Place a warm cookie, scoop of ice cream on top, and drizzle with chocolate sauce. Alternatively, enjoy it open-faced!
