In a medium bowl, toss the chicken cubes with 1 tablespoon olive oil, minced garlic, Italian seasoning, salt, and pepper. Ensure the chicken is evenly coated with the spices.

Heat the remaining 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the chicken and cook, stirring occasionally, until it is cooked through and lightly browned on all sides (about 5-7 minutes). Be careful not to overcrowd the pan; cook in batches if necessary to ensure even browning.

In a separate bowl, combine the mayonnaise and grated Parmesan cheese. Mix well until smooth and creamy.

Warm the tortillas in a dry skillet or microwave for a few seconds each to make them more pliable.

Spread a thin layer of the garlic cheese sauce evenly over each tortilla. Top with ¼ of the cooked chicken and ¼ of the shredded Monterey Jack cheese.

Fold in the sides of the tortilla, then tightly roll it up from the bottom.

Brush the outside of each wrap with melted butter (if using). Heat a large skillet over medium heat. Place the wraps in the skillet, seam-side down, and cook for 2-3 minutes per side, or until golden brown and crispy.

Cut the wraps in half and serve immediately.