Heat olive oil in a large skillet over medium-high heat. Add chicken cubes and cook until browned and cooked through, about 5-7 minutes. Season with Italian seasoning, salt, and pepper.

Add minced garlic to the skillet and cook for 1 minute until fragrant. Pour in chicken broth and bring to a simmer, scraping up any browned bits from the bottom of the pan. Cook until the broth has mostly evaporated, about 2-3 minutes.

Remove skillet from heat. Stir in mozzarella and cheddar cheese until melted and well combined with the chicken. If using, stir in softened cream cheese for extra creaminess.

Warm tortillas according to package directions (microwave for 15-20 seconds or briefly heat in a dry skillet).

Divide the chicken and cheese mixture evenly among the warmed tortillas. Fold in the sides of each tortilla, then roll it up tightly from the bottom to form a wrap.

Optional: For a crispy exterior, lightly brush the outside of the wraps with a little olive oil or butter before toasting them in the skillet or air fryer. Alternatively, you can bake them at 375°F (190°C) for 10-12 minutes.

Serve immediately, garnished with fresh parsley if desired.