In a large mixing bowl, beat heavy cream until stiff peaks form.
Add vanilla, and beat until just combined.
Stirring by hand, slowly add the condensed milk to the heavy cream mixture, folding gently to combine.
Gently fold in Nutter Butter cookies.
Spread mixture evenly into the bottom of an 11x7-inch glass baking dish.
In a small microwave-safe bowl, heat the peanut butter until thin and liquidy, but not scalding hot, about 30 seconds; set aside.
In a small microwave-safe bowl, heat the preserves until thin and liquidy, but not scalding hot, about 30 seconds.
Drizzle the peanut butter and preserves over the ice cream, and swirl with a knife to lightly incorporate.
Cover with plastic wrap and freeze until firm, at least 4 hours.