Combine the flour, sugar, salt, and yeast into a large bowl or the bowl of your stand mixer. Give all of the dry ingredients a good stir. Then add olive oil and water. 

If using a stand mixer, using your dough hook, mix on medium speed for 8 minutes or until the dough is smooth and pulled away from the bowl. After the mixer has done its work, turn the dough out onto a lightly oiled or floured surface and knead with your hands until you have a nice smooth, round dough ball - one or two minutes.

If you're kneading by hand, stir all the ingredients in the bowl until combined, and knead with your hands on a lightly flour-dusted counter for 10 minutes or until you have a smooth dough. Try to add as little flour as possible at this point. The dough will be sticky at first and get all over your hands, but keep mashing it and rolling it, and kneading it and after a few minutes, it will start to be less sticky. 

Shape your dough into a ball and place it in a lightly greased/oiled bowl in a warm place for 1 to 1.5 hours.

After the dough has almost doubled in size, turn it out onto a lightly floured or oiled surface. Divide into three equal pieces (use a scale if you want perfect sizes).

Press each dough piece with your fingers until you have a rectangle of about half the length that you want (in this case, around 5 or 6 inches since we're making 12-inch rolls) and about 3 inches wide. Roll the flattened rectangle up from the long side to the other long side until you have a log that is about 6 inches long and 1.5 to 2 inches around. Pinch the seal closed very well from one end of the seam to the other. This is important and helps the top of your dough log to stay tight. 

After I seal the seam, I roll the log over and over and carefully stretch the dough log until it's around 12 inches long. Do this for each of your 3 dough portions and place on a parchment-lined sheet pan. If you're using a silicone sub-roll mold, place each dough log in the mold with the mold placed in a sheet pan. Place each dough log pinched seam side down. 

Flatten each dough log with your fingers slightly so that it doesn't rise into quite a round cylinder. This will help the roll to be shaped better for sandwiches.

Cover your sheet pan with a lightly oiled/greased plastic wrap and place in a warm area for 1 hour. 

Preheat oven to 375F (190 C).

Right before baking, mix up your Italian herb and cheese topping mixture. This is the Italian seasoning, garlic powder, Parmesan cheese, and shredded cheese. Note: amounts of each ingredient are per roll. So if you're just making 3 rolls, add each ingredient 3 times. Mix the ingredients together and then spray water on top of each roll or paint water on with a brush, and sprinkle the tops evenly with the mixture.

Bake for 25 to 30 minutes, rotating the pan 180 degrees at the halfway point. (Note: this time is for non-convection ovens. If I use the convection setting it could cut as much as 8 minutes off the bake time.) Just take a peek at it when you turn the bread at the halfway point, and if it's already fairly tan, you might want to keep an eye on it. Your sub rolls need an internal temperature of 190 F (88 C) to be fully cooked.

Allow bread to cool before slicing.