1. Combine Wet Ingredients and Discard: In a large mixing bowl, whisk together the warm water, sourdough discard, granulated sugar, and salt until well combined. The discard doesn’t need to be perfectly dissolved, just mostly incorporated.

2. Add Flour and Mix Dough: Gradually add the all-purpose flour, one cup at a time, mixing with a wooden spoon or your hands until a shaggy dough forms. Once all the flour is added, knead the dough gently in the bowl for about 2-3 minutes until it just comes together. It will still be a bit sticky.

3. First Rise (Bulk Fermentation): Drizzle 2 tablespoons of olive oil into a clean large bowl, turning the dough to coat it. Cover the bowl tightly with plastic wrap or a damp kitchen towel. Place it in the refrigerator for 8-12 hours (or up to 24 hours) for its slow overnight proof. The dough will slowly rise and develop flavor.

4. Shape the Bread Bowls: The next day, remove the dough from the refrigerator. Gently punch it down and divide it into 4-6 equal pieces, depending on your desired bowl size. Shape each piece into a tight, round ball, pulling the edges underneath to create a smooth top surface.

5. Second Proof: Place the shaped dough balls onto a baking sheet lined with parchment paper, leaving ample space between them. Cover loosely with plastic wrap or a clean kitchen towel and let them rest at room temperature for 30-60 minutes, or until slightly puffy. Towards the end of this proofing time, preheat your oven to 400F (200C).

6. Bake to Golden Perfection: If using, brush the tops of the dough balls with the beaten egg wash for a golden crust. Bake for 25-30 minutes, or until the bread bowls are deep golden brown and sound hollow when tapped on the bottom.

7. Cool and Hollow Out: Once baked, transfer the bread bowls to a wire rack to cool completely. Once cool enough to handle, use a sharp serrated knife to carefully cut a circle from the top of each bread bowl. Scoop out the soft interior bread, leaving a sturdy shell about 1/2 to 3/4 inch thick. Save the scooped-out bread for croutons or snacking!