Preheat your griddle to medium. Add cooking oil of choice and the chicken. Season chicken with kosher salt, pepper, and Italian seasoning. Cook chicken 7 to 8 minutes, mixing a few times with spatulas.
Put butter, garlic, more kosher salt, pepper, and Italian seasoning in a small saucepan. Put the saucepan on the griddle as the chicken cooks, stirring a few times.
Turn griddle off, squeeze some of the lemon on the chicken and into the butter.
Place 4 ciabatta roll halves into the cast iron pizza dish, cut side up. Spoon half of the garlic butter onto each roll, add some alfredo sauce, half of the chicken, half of the cheese, more alfredo sauce, Italian seasoning, a squeeze of lemon, and parsley if using.
Preheat your Blackstone outdoor pizza oven to 400 degrees, place the dish into the pizza oven, with stone rotating, for 3 to 5 minutes until cheese is melted. Repeat making the four remaining garlic bread pieces.
Serve with leftover lemon wedges to squeeze over top.