For the omelet, heat the 2 tablespoons of olive oil in a large skillet over medium-high heat. Add the pancetta, green peppers and onions. Sauté until softened, about 5 minutes. Add the garlic and sauté another minute. Remove from heat. Beat the eggs in a large bowl. Add the sautéed vegetables, herbs, salt, pepper and Parmesan cheese. Stir well to combine. Reheat the skillet with the additional 2 tablespoons of oil over medium heat. Add the egg mixture and cook until the bottom is set. Cut into 6 wedges and turn each over to cook the other side. Remove from heat while preparing the spinach.
For the spinach, whisk the garlic, vinegar, mustard, salt, pepper and olive oil in a medium bowl until well-combined. Add the spinach and toss.
To assemble, split the rolls horizontally and, if desired, remove some of the bread from the inside. Spread some mayonnaise on the cut sides of each roll. Place a piece of omelet on the bottom halves. Top with the cheese, then some peppers and spinach. Top with the remaining roll halves and serve.