Preheat the oven to 350 degrees F. Spread the pretzels out, in one even layer, onto a foil-lined (or parchment-lined) baking sheet. Transfer the pretzels to the oven and toast until dark brown, about 10 minutes. Once they're done, remove them from the oven and set them aside until they're completely cooled. Add the cooled pretzels and whole milk to a bowl and allow to sit for 5 minutes. Pour the milk through a sieve, catching and discarding the soggy bits and pretzels. You should have 1 cup of pretzel milk remaining. If you have more, only use 1 cup and drink the rest--it's delicious. To the pretzel milk, add the egg, butter and vanilla extract; beat until completely combined.
In a medium bowl, mix together the flour, sugar, baking powder and salt. All at once, add the wet ingredients to the dry ingredients and mix until just combined. The batter should have some small to medium lumps.
Preheat your skillet over medium heat and brush with 1 1/2 teaspoons of butter or a teaspoon of vegetable oil. Using a tablespoon measure, scoop the batter onto the warm skillet. Add 3-4 pretzel pieces to each pancakes, gently pressing them into the pancake. Cook for 1 to 2 minutes until small bubbles form on the surface of the pancakes, and then flip. Reduce the heat to medium-low and cook on the opposite side for about 1 minute, or until golden brown.
Transfer the cooked pancakes to a baking sheet and place in a preheated 200 degree F oven to keep warm. Repeat the process with the remaining batter, adding more butter or vegetable oil to the skillet when needed. Serve immediately.
