Pour 2 cups hot water into bowl of electric mixer with dough hook. Check water with instant-read thermometer to register about 110 degrees. Add sugar, stir to dissolve. Sprinkle with yeast; let sit 5 minutes; yeast should bubble.
Beat 1 cup flour into yeast on low until combined. Beat in salt and 4 cups flour until combined, about 30 seconds. Beat on medium-low until dough pulls away from sides of bowl, about 1 1/2 minutes. Add 1/2 cup flour, and knead on low 1 minute more. If dough is still wet and sticky, add 1/2 cup more flour (this will depend on weather conditions); knead until combined, about 30 seconds. Transfer to a lightly floured board, and knead about 10 times until smooth.
Pour oil into a large bowl; swirl to coat sides. Transfer dough to bowl, turning dough to completely cover all sides. Cover with a kitchen towel, and leave in a warm spot for 1 hour, or until dough has doubled in size.
Heat oven to 450 degrees. Lightly spray two baking sheets with cooking spray. Set aside. Punch down dough remove bubbles. Transfer to a lightly floured board. Knead once or twice, divide into sixteen pieces (about 2 1/2 ounces each), and wrap in plastic.
Roll one piece of dough at a time into an 18-inch-long strip. Twist pretzel shape; transfer to prepared baking sheet. Cover with a kitchen towel. Continue to form pretzels; eight will fit on each sheet. Let dough rest until it rises slightly, about 15 minutes.
Meanwhile, fill large shallow pot with 2 inches water. Bring to a boil. Add baking soda. Reduce to simmer; transfer three to four pretzels to water. Poach 1 minute. Use slotted spoon to transfer pretzels to baking sheet. Continue until all pretzels are poached.
Beat egg with 1 tablespoon water. Brush pretzels with egg wash. Sprinkle with salt. Bake 12 to 15 minutes, until golden brown. Let cool on wire rack. Pretzels are best when eaten the same day, and will keep at room temperature, uncovered, for two days. Do not store in covered container.