Line a large baking pan with parchment paper. Place about 60 square pretzels in an even layer on top. Set aside.
In a large mixing bowl, beat the peanut butter and butter on medium speed until creamy, about 3 minutes. Add the vanilla and beat until incorporated, about 1 minute. Slowly add the powdered sugar one cup at a time until it's incorporated. Peanut butter mixture should be thick and slightly wet but not sticky.
Use a large rounded teaspoon to roll peanut butter mixture into balls. Place one ball of peanut butter on top of each pretzel prepared on the baking sheet. Once all balls are rolled, place another pretzel on top and gently press down to sandwich the peanut butter, being careful not to break the pretzels.
Once all sandwiches are made, combine the chocolate chips and oil in a large tall measuring cup and heat in the microwave on high in 30 second increments until chocolate is melted.
One at a time, dip half of each peanut butter pretzel sandwich into the chocolate and place back on the parchment paper. Repeat until all sandwiches are dipped. Place in the freezer for 15 minutes, or until chocolate is frozen.
Store in an air tight container in a cool place for up to 5 days or in the freezer for a month.