Warm 1 tablespoon of olive oil in a large non-stick skillet over medium heat.
Add the chicken breast strips to the skillet and sprinkle with fine sea salt, black pepper, dried oregano, and smoked paprika.
Cook the chicken for about 8–10 minutes, stirring occasionally, until it is cooked through and lightly golden at the edges.
Stir in the minced garlic and cook for 1 minute more, just until fragrant, then remove the skillet from the heat and set the chicken aside.
In a medium bowl, combine the plain Greek yogurt, mayonnaise, and grated Parmesan cheese, mixing until smooth to form a garlic cheese sauce.
Place the flour tortillas on a clean work surface and spread a generous spoonful of the garlic cheese sauce down the center of each tortilla.
Divide the shredded lettuce and diced tomato evenly over the sauce on each tortilla.
Spoon the warm cooked chicken strips over the vegetables, dividing the chicken evenly between the four tortillas.
Sprinkle the shredded mozzarella cheese evenly over the chicken in each wrap.
Fold the sides of each tortilla slightly inward, then roll them up tightly from the bottom to form wraps.
Add the remaining 1 tablespoon of olive oil to a clean skillet and warm it over medium heat.
Place the wraps seam-side down in the skillet and cook for 2–3 minutes per side, until the tortillas are lightly crisp and the mozzarella cheese is melted inside.
Remove the Cheesy Garlic Chicken Wraps from the skillet, let them rest for 1–2 minutes, then slice in half if desired and serve warm.