Preheat oven to 400 F (205 C).
Add a teaspoon of olive oil and balsamic vinegar to a parchment-lined sheet pan. Sprinkle salt and pepper on top of the oil and vinegar.
Top the seasoned oil and vinegar with thin slices of onion. Pile shredded cheese on top of the onion. Try to keep the onion and cheese within a 3 x 4-inch area.
Cut out a 3 x 4-inch rectangle of pizza dough and use it to cover the onion and cheese.
REPEAT the above process for a second slice of dough. Each sandwich will use two pieces of baked dough with onion and cheese as the bread. One for the top and one for the bottom of the sandwich.
Create an egg wash with the whole egg and a tablespoon of water. Whisk to combine. Paint the egg wash on top of each piece of dough. This will help the dough brown. Add salt and pepper to the top of the egg wash if desired.
Bake at 400 F (205 C) for 18 to 20 minutes rotating the pan halfway through the cooking time. When they are done, carefully move the baked dough to a rack to cool.
Sandwich assembly: in a small bowl, toss arugula in a teaspoon of olive oil and a teaspoon of balsamic vinegar. Add a pinch of salt and ground black pepper to season the arugula. Toss the greens to coat in the simple dressing.
Flip over one cheesy pizza dough onion tart so that the onions are facing up and add dressed arugula on top.
Top the arugula with slices of cantaloupe and then top the cantaloupe with slices of prosciutto.
Complete the sandwich with a second slice of pizza dough onion tart with the onions facing downward.
Serve and enjoy.
Notes:
You can make 4 sandwiches out of the amount of dough that comes in one of the store-bought pizza dough tubes. They are roughly 9x13 inches in size. If you want to make your own pizza dough, that's the size of a rectangle that you can shoot for with a dough thickness of less than a half inch.