In a large mixing bowl, combine the shredded chicken with the basil pesto, making sure the chicken is well coated. Season with salt and pepper to taste.
Lay out the tortillas or wrap breads on a clean surface.
In the center of each wrap, layer the arugula or spinach, followed by the pesto chicken mixture.
Add the halved mozzarella balls and cherry tomatoes on top of the chicken.
Drizzle a bit of balsamic glaze over the filling for a touch of sweetness.
Carefully fold in the sides of each tortilla, then roll them up tightly from the bottom to form wraps.
If desired, drizzle a little olive oil on top of the wraps for extra flavor before slicing them in half.
Notes
Arrange the wraps on a platter, drizzling additional balsamic glaze over the top and garnishing with fresh basil leaves for a pop of color.