Pour warm water and 1 tablespoon sugar into bowl of electric mixer fitted with a dough hook* and stir to combine. Sprinkle with yeast, and let sit 10 minutes; yeast should be foamy.

Add 1 cup flour to yeast, and mix on low until combined. Add salt and 4 cups more flour, and mix until combined, about 30 seconds. Beat on medium-low until dough pulls away from sides of bowl, about 1 1/2 minutes. Add another 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 ten times, or 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°F. Lightly spray two baking sheets with cooking spray (parchment paper, ungreased, also works). Set aside. Punch down dough to remove bubbles. Transfer to a lightly floured board. Knead once or twice, divide into 16 pieces (about 2 1/2 ounces each) or 32 if making miniature pretzels, and wrap in plastic.

Roll one piece of dough at a time into an 18-inch-long strip. Twist into pretzel shape; transfer to prepared baking sheet. Cover with a kitchen towel. Continue to form pretzels; eight will fit on each sheet (you may need a third sheet if making miniatures). Let pretzels rest until they rise slightly, about 15 minutes.

Meanwhile, fill large, shallow pot with 2 inches of water. Bring to a boil. Add baking soda (and step back, it foams up quickly) and remaining 2 tablespoons sugar. Reduce to a simmer; transfer three to four pretzels to water. Poach 1 minute on each side. 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 glaze. Sprinkle with salt. Bake until golden brown, 12 to 15 minutes. Let cool on wire rack, or eat warm. Pretzels are best when eaten the same day, but will keep at room temperature, uncovered, for two days.