In a large mixing bowl, combine the active sourdough starter and warm water. Stir until the starter is mostly dissolved. Add the bread flour and salt. Mix with a spoon or your hands until a shaggy dough forms and no dry flour remains. Cover the bowl with a damp cloth or plastic wrap and let it rest for 30 minutes (autolyse).

After the autolyse, add the 15g olive oil to the dough. Knead gently for 2-3 minutes directly in the bowl until the oil is incorporated and the dough starts to smooth slightly. Cover and let rest for 30 minutes.

Perform the first set of stretch and folds. With wet hands, gently grab a portion of the dough, stretch it upwards, and fold it over itself. Rotate the bowl 90 degrees and repeat 3 more times until you've gone around the entire dough. Cover and rest for 30-45 minutes. Repeat this stretch and fold process 3 more times (for a total of 4 sets), resting 30-45 minutes between each set.

After the final set of stretch and folds and rest, gently flatten the dough slightly. Sprinkle the Italian seasoning, garlic powder, onion powder (if using), and shredded cheese evenly over the surface. Gently fold the dough over itself a few times, performing a few more gentle stretch and folds to evenly distribute the inclusions without tearing the dough too much. Be careful not to overmix.

Cover the bowl and let the dough bulk ferment at room temperature (around 72-78°F / 22-25°C) for another 1.5-2.5 hours, or until it has increased in volume by about 20-30% and feels airy. The total bulk fermentation time from step 1 should be around 3-5 hours, depending on your starter's activity and ambient temperature.

Lightly flour your work surface. Gently turn the dough out onto it. Divide the dough into 8 equal pieces (approx. 110-120g each). Gently pre-shape each piece into a loose ball or cylinder. Cover with a damp cloth and let rest for 15-20 minutes to relax the gluten.

Lightly flour your hands. Take one pre-shaped dough piece. Gently flatten it into a rectangle. Fold the top edge down to the center and press to seal. Fold the bottom edge up to meet the top fold and press to seal. Pinch the seam closed firmly. Roll the dough piece gently back and forth on the work surface to create an even, elongated sub roll shape (about 6-8 inches long). Repeat with the remaining dough pieces.

Lightly dust a baking sheet with semolina or cornmeal, or line with parchment paper. Carefully transfer the shaped rolls to the prepared baking sheet, leaving space between them. Cover loosely with plastic wrap or a large inverted container to prevent drying. For cold proofing (recommended for flavor and easier scoring), refrigerate for 8-12 hours (or up to 24 hours). For warm proofing, proof at room temperature for 1.5-2.5 hours, or until visibly puffy and slightly increased in size. Perform a gentle poke test – if it springs back slowly, it's ready.

About 30-45 minutes before baking, preheat your oven to 450°F (232°C). If you desire a crispier crust, place a shallow pan on the bottom rack for creating steam.

If cold-proofing, remove rolls from the fridge. In a small bowl, whisk together the egg and water for the egg wash (if using). Gently brush the tops of the rolls with the egg wash. Optionally, use a sharp knife or bread lame to make 2-3 shallow diagonal scores on the top of each roll.

Carefully transfer the baking sheet to the preheated oven. If creating steam, pour about 1/2 cup of hot water into the shallow pan on the bottom rack (be careful of steam!). Immediately close the oven door. Bake for 10 minutes at 450°F (232°C). Reduce oven temperature to 400°F (200°C), remove the steam pan (if used), and continue baking for another 15-20 minutes, or until the rolls are golden brown, sound hollow when tapped on the bottom, and reach an internal temperature of 200-210°F (93-99°C).

Transfer the baked rolls to a wire rack to cool completely before slicing and serving. This allows the internal structure to set.