In the bowl of a standing mixer, combine the warm water and the dry active yeast and let side for 10 minutes to proof.
Add the sourdough starter discard and stir until it dissolves into the yeast mixture.
In a separate mixing bowl, combine the flour, sugar, and salt. Pour into the standing mixer bowl and start mixing on low.
Add the vegetable oil and continue to mix until the dough pulls away from and cleans the sides of the bowl.
Turn out dough onto a lightly greased surface and shape into a ball.
Transfer the dough to a lightly greased container. Cover and let rest for 45 minutes.
Turn the dough out onto a lightly greased surface and divide into 12 pieces, about 107 grams per piece.
Shape each piece into an 18-inch long rope and then twist the rope into a pretzel shape.
Place each pretzel onto a lightly greased parchment paper on a baking sheet.
Brush beaten egg over the pretzels, and sprinkle with sea salt or pretzel salt according to taste.
Preheat the oven to 350° F (176° C) and bake for 25 to 30 minutes.
Place pretzels on wire cooling rack to cool.