Line a baking sheet with parchment paper and set it aside.
Place all of the meatball ingredients into a large bowl. With clean hands, mix and fold the ingredients together until they're well blended. (Using your hands works much better than a spoon or spatula!)
Once blended, scoop up about 2 tablespoons worth of the meat mixture and roll it into a firm ball. Place it onto the parchment-covered baking sheet when done. Repeat until you get through all of the meat.
Place the meatballs in the fridge for at least 30 minutes; you can leave them in there for a few hours if you're working ahead of schedule.
Heat 1-2 tablespoons of olive oil in a large skillet or braiser over moderate heat. Carefully place the meatballs into the skillet one at a time. Cook the meatballs for 3-4 minutes per side, or until golden brown. When flipping the meatballs over, be gentle with them. Silicone tongs work really well. If the meatballs are sticking to the pan, let them cook for a little bit longer until they release. Don't force them or they'll fall apart.
Once the meatballs are lightly browned, add the pasta sauce to the skillet and bring to a simmer. Once the sauce is simmering, bring the temperature to low and simmer until the internal temperature of the meatballs reaches 145º F. When they do, remove them from the heat.
Slice into the sub sandwich buns 3/4 of the way, leaving the bottom of the buns intact. This will keep the ingredients nice and snug inside the buns, preventing everything from falling out when you bite into it.
Place two slices of cheese along the length of the inside of the buns. Scoop the meatballs and your desired amount of sauce into the buns, followed by your desired amount of bell peppers, onions, peppers, and fresh herbs.
Serve hot, in full length or cut into halves.