In a medium bowl, combine warm water, granulated sugar, and active dry yeast. Stir gently and let sit for about 10 minutes, or until the mixture is foamy and creamy.

In a large mixing bowl, whisk together flour, the remaining granulated sugar, and kosher salt. Make a well in the center and pour in the yeast mixture and vegetable oil. Mix with a wooden spoon until a rough dough forms.

Turn the dough out onto a lightly floured surface and knead for about 7 minutes, or until smooth and elastic. If the dough feels dry or stiff, sprinkle in a tablespoon or two of warm water and knead it in.

Lightly oil a clean bowl. Place the dough into the bowl and turn it to coat. Cover with plastic wrap or a clean kitchen towel and let rise in a warm spot for about 1 hour, or until doubled in size.

Preheat the oven to 450°F. Line two baking sheets with parchment paper and set aside.

In a large bowl, combine hot water and baking soda, stirring until the baking soda is dissolved. Set aside.

Punch down the dough and transfer it to a lightly floured surface. Divide into 12 equal pieces. Roll each piece into a rope about 18 inches long, then form into a pretzel shape by making a U, twisting the ends twice, and folding them down onto the bottom.

Using a slotted spatula or tongs, dip each pretzel into the baking soda water for 10–15 seconds, then place on the prepared baking sheets.

In a small bowl, whisk together the egg and water. Use a pastry brush to lightly coat each pretzel with the egg wash. Sprinkle the tops with kosher salt.

Bake for 8 to 10 minutes, or until golden brown.