Preheat your oven to 375 degrees F. Line a baking sheet with parchment paper and spritz with non-stick cooking spray.
Unroll the pizza dough on a large board. Press it out into a 10-inch x 15-inch rectangle using your hands.
Combine the chicken, BBQ sauce, and butter in a medium mixing bowl. Then spread the mixture over the pizza dough, leaving a 1-inch border at one of the short ends. Sprinkle the cheddar, mozzarella, and pepper jack cheese over the chicken filling.
Fold the short end with filling over about 2 inches, then fold in the sides and pinch the ends to keep the filling closed inside. Then roll up the dough and pinch the seam to the dough to seal it. Place on the prepared baking sheet, seam side down.
Mix the parmesan cheese and Italian seasoning together in a small bowl. Brush the top of the bread with the beaten egg and sprinkle with the Parmesan mixture. Cover loosely with foil.
Bake for 20 minutes, and then remove the foil and bake for another 15 minutes.
Remove from the oven and transfer the bread to a cutting board. Use a serrated knife to slice into 8 pieces. Serve warm with BBQ sauce or ranch dressing for dipping if desired.
Notes
If you prefer to use homemade pizza dough or pizza dough from your local pizzeria, you can. Just be sure to roll it out into a rectangle about 15 inches x 10 inches.