Combine the milk, egg, oil, sugar, flours, vital wheat gluten, salt, and yeast in the pan of your bread machine according to the manufacturer’s directions. Set on the dough cycle and start the machine.
To make the dough by hand or a stand mixer
Place the milk, sugar and yeast in a large bowl or the bowl of a stand mixer. Stir and allow the yeast to proof for 5 minutes.
Add the egg, oil, flours, vital wheat gluten, and the salt. Stir to combine well.
Knead by hand or with a dough hook to create a smooth, elastic dough, adding more of the all-purpose flour as necessary.
Transfer the dough ball to a greased bowl and turn it to coat. Cover and allow it to rise until doubled in bulk, about 1 hour.
To form the sub rolls
Line a large baking sheet with parchment paper or a silicone baking mat.
When the machine beeps or the dough has doubled in bulk, remove the dough from the pan and divide it into eight equal parts. Form each part into a long, thin oval and place equidistant apart on the prepared baking sheet.
Allow the rolls to rise for 20 minutes or longer, until doubled in bulk.
Preheat the oven to 350ºF.
Bake the rolls for 15 to 20 minutes until golden brown. Cool on a rack before serving.
Nutritional values are approximate and are based on making 8 rolls from the recipe. Use within 4 days. Store in an airtight container.