In the Kitchen Aid bowl (or a large mixing bowl), pour in 1 1/2 cups warm water and 1 tablespoon of sugar, then sprinkle in 2 ¼ teaspoons of instant yeast and let it rest for 5 minutes (or 15 minutes for regular yeast) to activate.
Stir in the 1 teaspoon of salt and 2 tablespoons of melted and cooled vegan butter. Slowly stir in 3 1/4 cups of bread flour until combined.
Using a KitchenAid mixer fitted with a dough hook, knead the dough for 4-5 minutes, sprinkling in up to 1/2 cup of additional flour as needed until the dough is no longer sticky. (Or knead the dough on a clean, floured surface for 5 to 8 minutes each time the dough feels sticky, add more flour, 1-2 tablespoons at a time.)
Shape the dough into a ball and place it in a clean and lightly oiled large bowl. Cover the bowl with plastic wrap or a damp kitchen towel, then place it in a warm area to rise for 60 to 90 minutes, or until the dough has doubled in size.
While the dough is rising, line 2 baking sheets with parchment paper and set aside.
Once the dough has risen, bring 5 cups of water to a boil and slowly add in 1/4 cup of baking soda to create a baking soda bath. And Preheat oven to 400ºF.
Cut the risen dough into 4 pieces to make them easier to work with, then roll the pieces into a long rope. Cut each rope into 1/2 to 1-inch pieces with the bench scraper or kitchen scissors. (The pretzel bites will puff up and get bigger in the baking soda bath.)
Drop the pieces in the boiling baking soda water for approximately 30 seconds. Scoop them out with a slotted spoon and carefully line them on your parchment-lined baking sheet. Repeat this process until the baking sheet is full. Sprinkle each piece with pretzel salt.
Bake at 400ºF for 14 minutes, or until the tops are brown. While the first batch is baking, work on the remaining half of the dough.