Heat a skillet over medium heat and add a small amount of oil. Place the seasoned chicken into the pan and cook for several minutes on each side until it is fully cooked, golden on the outside, and juicy on the inside. Once done, remove it from the pan, let it rest briefly, and then slice or shred it into bite-sized pieces.
In a mixing bowl, add Greek yogurt along with minced garlic, a pinch of salt, and black pepper. Stir everything together until the mixture becomes smooth, creamy, and well combined, creating a flavorful garlic sauce.
Add the cooked chicken pieces into the bowl with the garlic sauce, then sprinkle in the shredded cheese. Mix everything together gently until the chicken is evenly coated and the cheese is distributed throughout the mixture.
Lay a wrap flat on a clean surface and spoon the chicken mixture onto the center. Spread it evenly, leaving a little space around the edges. Fold the sides inward and then roll the wrap tightly to secure the filling inside.
Place the filled wraps onto a heated pan over medium heat. Cook for a few minutes on each side, pressing lightly, until the outside becomes golden brown and slightly crispy, and the cheese inside melts.
Remove the wraps from the pan and let them cool for a minute. Slice if desired and serve warm while the texture is crispy on the outside and creamy on the inside.