Combine peanut butter, butter, vanilla and salt in large bowl. Beat with an electric mixer on LOW until blended.
Add 2 cups powdered sugar, beating until blended. Beat in the last cup of powdered sugar until combined.
Shape into 1-inch balls. Sandwich/squeeze each peanut butter ball between two pretzels. Place on baking sheets fitted with a silicone baking mat, parchment paper, or wax paper. Freeze for 15 minutes or refrigerate for 30 minutes.
Place chocolate chips and coconut oil or shortening in a double boiler. (Or stainless steel bowl on top of a saucepan filled with water - make sure the water does NOT touch the bottom of the bowl!) Heat on medium-low until melted.
Dip pretzel bites halfway into the chocolate, shaking off any excess chocolate. Return to tray. Repeat until all pretzel bites have been dipped in chocolate. Place tray(s) back into fridge/freezer until chocolate is set, about 15 minutes. Store in an airtight container in the refrigerator up to 7 days.