Make the alfredo sauce: In a medium saucepan over medium heat, melt the butter. Add the minced garlic and cook for 1 minute until fragrant. Pour in the heavy cream and Italian seasoning. Let simmer for 2-3 minutes until slightly reduced. Turn heat to low and gradually stir in the Parmesan until melted and smooth. Season with salt and pepper. Set aside to cool slightly while preparing dough.

Prepare the dough: Cut the pizza dough into 4 equal pieces. On a lightly floured surface, use a rolling pin to roll each piece into a 6 inch round, about 1/4 inch thick. Transfer the rolled dough rounds to a parchment lined baking sheet.

Assemble the calzones: Spread 1/4 of the alfredo sauce on one half of each dough round, leaving a 1/2 inch border. Top sauce with 1/2 cup shredded chicken and 1/4 cup mozzarella. Fold the empty dough half over the filling, pressing and crimping the edges with a fork to seal securely.

In a small bowl, combine the softened butter and chopped parsley. Use a pastry brush to brush the top of each assembled calzone with the parsley butter.

Cook the calzones: Place calzones in air fryer basket lightly coated with oil or lined with parchment paper. Air fry at 375°F for 8 minutes until the crust is golden brown, flipping halfway through. Brush again with remaining parsley butter.

Let calzones cool for 5 minutes before serving. Enjoy with warm marinara sauce for dipping if desired. Leftover calzones can be refrigerated for up to 3 days or frozen for up to 3 months.