Add the chopped chicken, minced garlic, mayonnaise, yogurt, hot sauce, and salt to a mixing bowl. Stir everything together until the chicken is fully coated in that creamy, garlicky sauce. This mixture is really the heart of the whole wrap, so take a moment to taste and adjust the seasoning if needed.
Lay a tortilla flat on your counter or cutting board. Sprinkle a layer of cheese along the lower third, then spoon the chicken mixture right on top. Finish with another sprinkle of cheese and a bit of chopped green onion for freshness.
Fold the sides of the tortilla in toward the center to keep the filling from spilling out. From there, roll it up tightly starting from the bottom edge. Repeat the same process with your second tortilla so both wraps are ready to cook.
Heat a non-stick skillet over medium-high heat and give it a light spray of olive oil. Place the wraps seam-side down so they seal shut while cooking, then cover with a lid and cook a few minutes on each side. You're looking for a deep golden color and a crisp exterior.
Once both sides are golden brown, transfer the wraps to a cutting board. Slice them in half, straight across or on a diagonal, so you can see all that melty cheese inside. Serve them right away while everything is still warm and gooey.