Mix the dough. In a large bowl or stand mixer bowl, combine flour, yeast, sugar, and salt. Add warm water and olive oil. Mix until a shaggy dough forms, scraping down the sides as needed.
Knead until smooth. Knead with a dough hook on medium-low for 8 to 10 minutes, or by hand for 10 to 12 minutes, until the dough is smooth, elastic, and slightly tacky but not sticky. If it is sticking hard to the bowl or counter, add flour 1 tablespoon at a time.
First rise. Shape dough into a ball and place in a lightly oiled bowl. Cover and let rise until doubled, about 60 to 75 minutes (warmer kitchens go faster).
Divide and pre-shape. Turn dough onto the counter and divide into 6 equal pieces. Shape each into a tight ball, cover, and rest for 10 minutes. This makes shaping easier and keeps the dough from fighting you.
Shape hoagie rolls. Flatten a piece into a rectangle (about 6 inches wide). Roll it up tightly from the long edge like a jelly roll, pinching the seam closed. Roll under your palms to about 8 to 9 inches long, tapering the ends slightly if you want the classic look. Place seam-side down on parchment-lined sheet pans, spaced apart.
Second rise. Cover loosely with oiled plastic wrap or a clean towel and let rise until puffy, about 35 to 50 minutes. When you gently press the side, it should slowly spring back.
Heat the oven and prep steam. While rolls rise, preheat oven to 425°F. Place an empty small metal pan on a lower rack (not on the oven floor). Avoid glass or ceramic here. Bring 1 cup of water to a boil.
Egg wash and score. Whisk egg with 1 tablespoon water. Brush tops gently. If you want a classic top slit, score each roll with one shallow cut lengthwise using a sharp knife or lame. Add sesame seeds if using.
Bake. Put rolls in the oven. Carefully pour the boiling water into the hot empty pan to create steam, then close the door. Watch your hands and face, the steam is intense. Bake for 16 to 20 minutes, rotating pans halfway, until deep golden brown. If you have a thermometer, aim for 195°F to 205°F internal depending on how soft or crusty you like them (higher end = a bit more structure and color).
Oven note: If your oven browns unevenly or feels crowded, bake one pan at a time for the best rise and most even color.
Finish and cool. Brush hot rolls with melted butter if you like a softer, shinier crust. Cool on a rack for at least 20 minutes before slicing so the crumb sets and stays fluffy.
Make-ahead option: After shaping (Step 5), cover the rolls and refrigerate 8 to 16 hours. The next day, let them sit at room temp until slightly puffy, usually 45 to 75 minutes, then continue with egg wash, steam, and baking.
Size options: For smaller lunch subs, divide into 8 rolls and shape to 6 to 7 inches. Start checking for doneness around 14 to 16 minutes.
Sandwich tip: For hot subs, split and toast the cut sides. For cold hoagies, keep the interior soft and swipe on mayo or oil first to create a little moisture barrier.
