For the dipping sauce: Whisk together the mustard, honey and horseradish in a bowl; season with salt and pepper. Cover and let sit at least 30 minutes before serving to allow the flavors to meld.
For the soft pretzels: Combine the sugar, salt, yeast and 1 1/2 cups warm water in the bowl of a stand mixer and mix with the dough hook until combined. Let sit 5 minutes.
Add the butter and 4 1/2 cups of the flour and mix on low speed until combined. Increase the speed to medium and continue kneading until the dough is smooth and begins to pull away from the sides of the bowl, 3 to 4 minutes. If the dough appears too wet, add additional flour a tablespoon at a time. Remove the dough from the bowl, place on a flat surface and knead the dough into a ball with your hands.
Oil a bowl with vegetable oil, add the dough and turn to coat with the 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 450 degrees F. Line 2 baking sheets with parchment paper and spray liberally with cooking spray.
Bring 3 quarts water to a boil in a large pot over high heat and add the baking soda.
Remove the dough from the bowl, place on a flat surface and divide into 8 equal pieces. Roll each piece into a long rope measuring about 22 inches. Shape each into an upside-down U shape, then bring the ends together and twist them to create a pretzel shape.
For the salt mixture: Combine the salt, black pepper and pink pepper in a small bowl; set aside.
Boil the pretzels in the water solution 2 at a time for 30 seconds; remove with a large flat slotted spatula or a spider.
Place 4 pretzels on each baking sheet, brush the tops with the egg wash and season liberally with the salt mixture. Bake until golden brown, 15 to 18 minutes. Remove to a baking rack and let rest 5 minutes before eating. Serve with the dipping sauce on the side