To a mixing bowl add the instant yeast, sugar, water, and sourdough discard. Whisk until mostly mixed.
Then add the flour, salt, and oil and mix until a shaggy dough is formed.
Cover the dough and let it rest for 15-20 minutes to hydrate and relax the gluten.
After the dough has rested, knead it into a smooth ball, about 3–6 minutes. You shouldn’t need much extra flour. If using a stand mixer, knead for the same amount of time.
Once kneaded, place the dough in a buttered or oiled bowl, cover, and let rise until doubled and puffy (about 2 hours).
Once the dough has doubled in size, line a large baking sheet with parchment paper.
Turn the dough out onto a lightly floured surface and divide it into 6 equal portions. Shape each piece into a round ball and let them rest for 10-15 minutes.
After the dough has rested, roll each ball into a rough rectangle (about 5x7 inches) and roll into a log.
Tighten the seams by pinching them together and ensure each log is around 6 inches long.
Place each shaped hoagie on the large baking sheet (spaced a few inches apart) and cover the pan with a damp tea towel, oiled plastic wrap, or a large proofing bag and let the dough rise until doubled (45-60 minutes).
Once the dough has finished its second rise, preheat the oven to 375 degrees F.
Place the dough in the freezer for 10-15 minutes to make scoring easier. While the dough is resting, whisk together 1 egg and a splash of water.
Remove the hoagies from the freezer and brush with the egg wash. Score 3 diagonal lines down each hoagie using a bread lame or sharp razor.
Bake the sourdough discard hoagies for 18-25 minutes or until golden brown.
Upon removing the hoagies from the oven brush them with butter for a softer crust. Allow them to cool completely before slicing and enjoying!
