In a medium bowl, combine the creamy peanut butter, powdered sugar, and vanilla extract. Mix until smooth and well combined.
Take one graham cracker and spread a generous layer of the peanut butter mixture on top. Place another graham cracker on top to create a sandwich. Repeat this process until all the peanut butter mixture is used.
In a microwave-safe bowl, combine the chocolate chips and vegetable oil. Microwave in 30-second intervals, stirring in between, until the chocolate is completely melted and smooth.
Dip each graham cracker sandwich into the melted chocolate, ensuring it is fully coated. Use a fork to lift it out and let any excess chocolate drip off.
Place the chocolate-coated sandwiches on a parchment-lined baking sheet. Once all are coated, refrigerate for at least 30 minutes to allow the chocolate to set.