In the bowl of a stand mixer combine 1 1/2 cups warm water, 2 tablespoons light brown sugar, 1 package active dry yeast, and 3 ounces unsalted butter (melted). Mix with the dough hook until combined. Let sit 5 minutes to activate the yeast.
Add 2 1/2 teaspoons kosher salt and 4 1/2 cups all-purpose flour to the mixer. Mix on low speed until the flour is incorporated. Increase speed to medium and knead with the dough hook until the dough is smooth and begins to pull away from the sides of the bowl, about 3 to 4 minutes. If the dough seems too wet, add additional all-purpose flour 1 tablespoon at a time, up to the remaining 1/2 cup (total 5 cups).
Remove the dough from the bowl and shape it into a ball by hand. Lightly coat a clean bowl with canola oil, place the dough inside, and turn to coat the dough with oil. Cover with a clean towel or plastic wrap and place in a warm spot until the dough doubles in size, about 1 hour.
Preheat the oven to 425°F. Meanwhile, in a large pot bring 5 quarts water to a boil over high heat. Carefully add 3/4 cup baking soda to the boiling water (it will foam) and return to a gentle boil.
Punch down the risen dough and transfer it to a lightly floured surface. Divide the dough into 8 equal pieces (about 4 1/4 to 4 1/2 ounces each). Roll each piece into a rope about 22 inches long, then cut each rope into 1-inch pieces.
Flatten each 1-inch piece with a rolling pin. Place small pieces of pepperoni and a pinch of shredded mozzarella cheese in the center of each flattened piece. Fold the dough over the filling and pinch the seams and ends firmly to seal, forming pretzel bites. Arrange the assembled bites on a baking sheet lined with parchment paper or a Silpat, keeping them from touching.
Working in batches (about 15 bites at a time), carefully lower the pretzel bites into the boiling baking-soda water and boil for about 30 seconds. Use a large slotted spoon to remove them and return them to the prepared baking sheet.
Brush the tops of the pretzel bites with the egg beaten with 1 tablespoon cold water. Sprinkle coarse sea salt over the tops.
Bake in the preheated oven for 15 to 18 minutes, or until the pretzel bites are golden brown.
Remove from the oven and let cool 5 minutes. Serve warm with pizza sauce.