1. Load the Bread Machine Pan: Begin by adding the warm water, active sourdough starter, and olive oil to your bread machine pan. It’s important to add liquids first, as per most bread machine instructions, to ensure proper mixing.

2. Add Dry Ingredients: Next, carefully add the bread flour, granulated sugar, and salt to the pan. Create a small well in the center of the flour mixture and add the instant yeast into this well. This keeps the yeast separate from the salt and liquids initially, which can sometimes inhibit its activation.

3. Start the Dough Cycle: Place the bread machine pan into the machine and select the “Dough” cycle. This cycle typically includes kneading, a first rise, and sometimes a punch-down. Let the machine complete its full cycle, which usually takes between 1.5 to 2 hours. The dough should be smooth, elastic, and have doubled in size.

4. Shape the Hoagie Rolls: Once the dough cycle is complete, carefully remove the dough from the bread machine pan and place it onto a lightly floured surface. Gently punch down the dough to release the air. Divide the dough into 6-8 equal pieces. For each piece, gently roll it into an oval or cylindrical shape, about 6-8 inches long, tapering slightly at the ends to resemble a classic hoagie roll.

5. Second Rise: Arrange the shaped rolls on a baking sheet lined with parchment paper, leaving some space between each roll. Cover the baking sheet loosely with a clean kitchen towel or plastic wrap. Let the rolls rise in a warm place for 30-45 minutes, or until they have visibly puffed up and look light and airy.

6. Prepare for Baking: Preheat your oven to 375 F (190 C) during the last 15 minutes of the second rise. If using, whisk the egg with a tablespoon of water to create an egg wash. Gently brush the tops of the risen rolls with the egg wash and sprinkle with sesame or poppy seeds, if desired.

7. Bake to Golden Perfection: Place the baking sheet in the preheated oven and bake for 15-20 minutes, or until the rolls are golden brown on top and sound hollow when tapped on the bottom. The internal temperature should be around 200-210 F (93-99 C).

8. Cool Before Serving: Once baked, transfer the hoagie rolls to a wire rack to cool completely. Cooling is crucial as it allows the internal structure to set, preventing a gummy texture. Slice them open and fill them with your favorite sandwich ingredients!