Pour 1/2 cup of the warm water into a small bowl. Gently stir in 1 tablespoon sugar and yeast. Let sit in a warm, draft-free spot, until foamy and frothy, about 10 minutes. If mixture doesn't foam, toss and start over.
In the bowl of an electric mixer, fitted with the dough hook, add the remaining water, 4 cups flour, salt, granulated garlic, parmesan, oil, and yeast mixture. Add as much of the remaining flour as needed until dough pulls away from sides of bowl. Knead on high until smooth and elastic, about 8 to 10 minutes. Transfer dough to a oiled bowl, turning over to coat both sides. Cover loosely with plastic wrap and a damp kitchen towel. Let rest in a warm spot until doubled in size, about 1 hour.
Heat oven to 375 degrees. Line two baking sheets with parchment paper and lightly grease with cooking spray. Punch down dough to release the air. Transfer to a lightly floured work surface and knead once or twice, divide dough into 16 even pieces. Working with one piece at a time, roll into an 18-inch-long strip. Twist into pretzel shapes and transfer to prepared baking sheets. Cover with plastic wrap and a kitchen towel. Let pretzels rest until they rise slightly, about 10 minutes.
Meanwhile, fill a large pot with 2 inches of water and bring to a boil. Add baking soda and remaining sugar. Reduce to a simmer. Carefully drop in 1 to 2 pretzels at a time and boil for about 30 seconds. Flip over the pretzels and cook for another 10 to 20 seconds. Use a slotted spoon to transfer pretzels back to the baking sheets. Continue until all pretzels are boiled.
Sprinkle the dough with mozzarella and parmesan cheese and top each with 2 to 3 pepperoni slices. Bake until golden brown and the cheese has melted, about 15 to 20 minutes. Remove from oven, let cool slightly and serve with pizza sauce on the side for dipping.
These pizza pretzels can be made in advance, stored in the freezer for up to 3 months and then rewarmed in oven when ready to eat!