Combine peanut butter, butter, and brown sugar in a microwave-safe bowl; heat in microwave until melted and evenly combined, about 45 seconds. Add graham cracker crumbs into a pie plate. Pour peanut butter mixture over graham cracker crumbs and stir. Flatten crust into the bottom and up the sides of pie plate using the back of a spoon.
Mix sweetened condensed milk, cream cheese, and chocolate syrup together in the bowl of a stand mixer on low speed until combined.
Combine dark chocolate chips, milk chocolate chips, and vegetable oil in a microwave-safe bowl; heat in microwave on 50% power until melted, stirring every 15 seconds, about 1 minute. Mix chocolate mixture into cream cheese mixture on low speed, scraping down sides of bowl as needed, until filling is smooth. Pour filling into crust and refrigerate until completely chilled, at least 2 hours.