Preheat oven to 350F. Line a baking sheet with parchment paper and set aside.
Beat egg and set aside.
Combine applesauce, oat flour, and rolled oats in a large bowl. Pour all but 1 tablespoon of the egg over the mixture and set aside the remaining 1 tablespoon of egg.
Using a wooden spoon, stir the mixture until a dough forms. The dough should be tacky but not overly sticky. Add a bit more or less flour if necessary.
Take a two tablespoon sized piece of dough (approximate) and roll into a tube. It should be about 10 inches long and about the width of a pencil.
Take each tube and make into a U shape, then twist the ends together and fold back to the top. This makes the pretzel shape. Pinch the ends in to make sure they're secure.
Place the pretzels onto the baking tray. Brush the top of each pretzel with the remaining egg.
Bake for approximately 25-30 minutes until they're slightly browned and become crispy. The pretzels should be pretty hard, just like pups love them!
Remove from the oven and allow to cool before serving.
Store in an airtight container for up to 2 weeks.