Preheat the oven to 400 degrees F.
Heat 1 tablespoon oil in a medium saute pan over medium heat. Add the onions, and saute until they become soft and caramelized, about 10 minutes. Remove from the pan, and set aside.
To the same pan, add the remaining tablespoon of oil and the red bell pepper and mushrooms. Season with a pinch of salt, and saute until the peppers are tender and the mushrooms have darkened a little, about 6 minutes.
For the kid version, cut 2 of the dough balls in half. You can either freeze the dough now, or make 4 small kid calzones and freeze two then. Up to you!
Once the dough is halved, roll out each ball into a 6-inch circle. Lightly spoon about 1 tablespoon of pizza sauce over each dough circle, and sprinkle about 1 tablespoon of mozzarella on top. Sprinkle 1/4 cup pepperoni over the cheese, and top with another tablespoon of mozzarella. Fold one end over the other, and crimp at the seams to close. Continue with the remaining three circles of dough. Transfer to a baking sheet lined with foil.
Now for the adult versions: Roll out the 2 remaining 8-ounce balls of dough into 8-inch circles, and spoon 2 tablespoons of sauce over the dough. Top with a tablespoon of mozzarella, followed by a small mound of caramelized onions and sauteed bell pepper and mushrooms. Finish with another tablespoon or so of mozzarella. Fold and crimp at the seams, as you did with the kid calzones. Transfer the two adult calzones to the baking sheet.
Brush the calzones with the beaten egg. Lightly sprinkle each calzone with a pinch of Parmesan. Add an additional sprinkling of Italian seasoning to the adult calzones. (So, so good.)
Bake the calzones until golden brown and cooked through, about 30 minutes. Serve with the remaining pizza sauce as a dipping sauce (or even ranch dressing, if you're awesome like that).