In a medium bowl, add the chopped chicken, softened cream cheese, shredded mozzarella, minced garlic, olive oil, and a pinch of salt and pepper. Stir until everything is evenly blended and creamy.

Lay a tortilla flat. Scoop a generous portion of the chicken mixture into the center, leaving room at the edges.

Fold the short sides in, then roll the tortilla tightly from one end to the other so the seam is on the bottom. Repeat with the remaining tortillas.

Warm a nonstick or cast-iron skillet over medium heat. Add a small drizzle of olive oil and swirl to coat.

Place the wraps seam side down in the skillet. Cook for 3 to 4 minutes per side, pressing gently with a spatula, until each side is golden brown and the cheese is melted inside.

Remove from heat, let the wraps rest for a minute, then slice in half on the diagonal. Garnish with chopped parsley if you like and serve warm.