In a large measuring cup, whisk yeast, sugar and 1 1/2 cup warm water. Please pay attention to the temperature of the water. That's what controls the yeast and helps it multiply. Temp should be between 105-110 degrees F. Let stand for 8-10 minutes until foamy and creamy. Then add oil, mix and set aside.
In a stand mixer using the hook attachment, combine your flour and 1 tsp salt. Slowly add your yeast mixture while stirring on low speed. Let mix for 10 minutes. In the meantime, lightly oil a large bowl.
Place dough in oiled bowl, turning to coat. Cover with plastic wrap and let rise for at least an hour until double in size. I let mine rise for about an hour and 15 minutes.
When risen, turn dough out onto a lightly floured surface, dividing dough into 8 pieces. Roll each piece into a rope. Starting at the center and moving your hands outward towards the ends. That will keep the whole 'rope' of even thickness. Twist into a pretzel shape.
Preheat oven to 450 degrees. Place foil onto a baking sheet and spray well with nonstick spray.
In a large sauce pan over medium heat, dissolve the baking soda in the 5 cups of water bringing it to a boil. Stir to dissolve. Let cool for 1 minute.
Dip each pretzel into the baking soda solution and fully submerge for 10 seconds. I used a slotted spatula to help hold it under. Then, using the spatula, remove the pretzel and place on the baking sheet. You may need ot fix the shape a little here. Repeat until sheet is filled. About 4 pretzels per sheet.
In a small bowl, beat the egg with 1 tbsp water until frothy. Brush over the top of each pretzel and sprinkle with salt.
Bake 8-10 minutes until lightly golden brown. Once done, brush with melted butter and sprinkle with salt. Serve warm with mustard and pub cheese.