In the bowl of a stand mixer, combine the warm water (it should feel like warm bath water) and yeast. Let this mixture sit for 10 minutes until it becomes foamy – this tells you your yeast is alive and active.

Add your room temperature sourdough discard to the yeast mixture. Using the paddle attachment, mix on low speed until well combined, about 30 seconds.

In a separate large bowl, whisk together the flour, table salt, and sugar until evenly distributed.

Switch to the dough hook attachment. With the mixer running on low speed, gradually add the dry ingredients to the wet mixture, about 1 cup at a time. This prevents flour from flying everywhere.

Once all flour is incorporated, add the vegetable oil and increase speed to medium-low. Mix for 5-7 minutes until the dough pulls away cleanly from the sides of the bowl and forms a smooth, slightly tacky ball.

Lightly grease a large bowl with oil. Transfer the dough to this bowl, turning it once to coat with oil. Cover with plastic wrap or a damp kitchen towel.

Let the dough rest at room temperature for 45 minutes. It won't double in size but will become slightly puffy.

Preheat your oven to 350°F and line two baking sheets with parchment paper.

Turn the dough out onto a clean, unfloured surface. Using a bench scraper or knife, divide the dough into 12 equal pieces (about 3.8 oz each if you're using a scale).

Working with one piece at a time, roll each portion into an 18-inch rope. If the dough resists rolling, let it rest for 5 minutes to relax the gluten, then try again. The rope should be about the thickness of your finger.

To shape each pretzel: Form a U-shape with the rope. Cross the ends over each other twice to form a twist, then bring the twisted end down to meet the bottom of the U. Gently press to seal.

Place shaped pretzels on the prepared baking sheets, leaving about 2 inches of space between each.

Beat the egg with 1 tablespoon of water to create an egg wash. Using a pastry brush, gently brush each pretzel with the egg wash, making sure to coat all exposed surfaces.

Sprinkle generously with coarse salt.

Bake for 25-30 minutes, rotating the pans halfway through, until the pretzels are deep golden brown. They should sound hollow when tapped on the bottom.

Transfer to a wire rack to cool for at least 5 minutes before serving. They're best enjoyed warm but will keep in an airtight container for up to 3 days.