Italian Peppers & Eggs Sandwich

An Italian favorite in the Philadelphia area. Good for breakfast or for lunch.
I've seen recipes where grated mozzarella cheese is added to the eggs at the end of scrambling. The heat from the eggs melts the cheese.
Variations: Add chopped pieces of ham with the peppers. You can also place a slice of mild provolone cheese on the bread and then top with the eggs for a Peppers & Eggs with Cheese.
4 large eggs
1 tbls. water
1/4 cup grated parmesan or romano cheese
Salt and pepper to taste
1 green or red pepper, washed, seeded and diced
1 medium onion, diced
1 clove garlic, chopped
1/4 cup olive oil (enough to coat bottom of pan)
1 loaf of Italian or French bread sliced to make 4 sandwich rolls
Parmesan cheese, optional
Crushed red pepper, optional
Mild or hot giardiniera (pickled vegetables including cauliflower and carrots), optional [or pickled hot peppers]
Beat the eggs with the water and parmesan cheese. Set aside.
In large hot skillet add olive oil, onion and peppers. Season with salt and pepper, stir to coat peppers with olive oil. Cook on medium heat, stirring frequently, until peppers start to soften and have browned a bit. Do not overcook; peppers should still have a bit of crunch. Add garlic.
Meanwhile, toast bread in a 400 degrees oven until crispy on the outside but still soft inside.
Lower heat and add eggs, stirring well to coat egg onto peppers. Cook eggs until set. Sprinkle with more parmesan cheese and red pepper flakes, if desired.
Cut the bread into 4 pieces. Slice the horizontally along one side, leaving the other long side still attached. Place some eggs in each sandwich roll. Add gardinera if desired.