Heat olive oil in a medium skillet over medium heat. Add cubed chicken and garlic. Season to taste with salt and pepper. Cook, stirring occasionally, until the chicken is cooked through and the garlic is fragrant, approximately 5-6 minutes. Remove from heat and set aside.
Preheat the oven to 400°F. Line a rimmed baking sheet with a piece of parchment paper for easy clean up.
Divide the pizza dough into 4 equal portions and roll out into 1/4-inch thick circles.
In a large mixing bowl, combine the cooked chicken, 1/4 cup of marinara sauce, pesto, mozzarella, parmesan, and fresh basil. Season with salt and pepper to taste.
Divide the filling between the 4 pizza rounds, spreading it only on one half of the dough. Fold the other side of the dough on top of the filling and pinch the edges to seal.
Arrange the calzones on the prepared baking sheet and brush with the beaten egg.
Transfer into the oven and bake until deeply golden on top, approximately 14-16 minutes
Allow to cool for at least 10 minutes.
Serve with the remaining marinara as a dipping sauce.
Enjoy!