Pound the Chicken Breasts: Place one chicken breast between two sheets of plastic wrap on a cutting board. Strike the thickest part with a meat mallet, working outward from the center in even strokes, until the breast reaches a uniform thickness of 1.5cm / 0.6in. Repeat with the second breast. Even thickness ensures both breasts finish cooking at the same time without the thin end drying out before the thick end is safe.
Apply the Spice Rub: Combine the smoked paprika, garlic powder, ground cumin, kosher salt, and black pepper in a small bowl and stir until the spices are evenly blended. Lay both pounded chicken breasts flat on the cutting board. Press the spice mixture firmly onto both sides of each breast, using your fingertips to work it into the surface. Let the seasoned chicken rest on the cutting board for 5 minutes so the salt begins drawing moisture to the surface, which improves crust formation during searing.
Sear the Chicken: Heat 1 tablespoon of olive oil in a 12-inch cast iron skillet over medium-high heat for 2 minutes until the oil shimmers and a drop of water flicked into the pan evaporates on contact. Place both seasoned chicken breasts in the skillet without overlapping them. Cook for 7 minutes on the first side without moving the breasts until a deep reddish-brown crust forms and the meat releases cleanly from the pan surface.
Finish and Check Temperature: Flip each breast using tongs and cook for 7 minutes on the second side. Insert an instant-read thermometer into the thickest part of one breast. The internal temperature must read 74°C / 165°F, and the juices running from the puncture point must run clear with no pink tint. Transfer both breasts to the cutting board and rest them uncovered for 5 minutes before slicing.
Slice the Chicken: Position one rested chicken breast on the cutting board with the long edge facing you. Use a sharp chef's knife to slice the breast against the grain into strips 1cm / 0.4in wide. Repeat with the second breast. Slicing against the grain shortens the muscle fibers and produces strips that stay tender when you bite through the wrap.
Make the Yogurt Sauce: Combine the Greek yogurt and fresh lime juice in a small bowl. Stir vigorously with a spoon for 30 seconds until the mixture is smooth and the lime juice is fully incorporated. The acid in the lime juice loosens the yogurt to a pourable consistency that spreads evenly across the tortilla without tearing it.
Warm the Tortillas: Place one flour tortilla in the dry cast iron skillet over medium heat for 30 seconds per side until the tortilla is pliable and faint golden spots appear on the surface. Transfer to a clean cutting board. Repeat with the remaining 3 tortillas, stacking them under a clean kitchen towel to retain their warmth and flexibility during assembly.
Assemble the Wraps: Lay one warm tortilla flat on the cutting board. Spread 1 tablespoon of yogurt-lime sauce across the center, leaving a 4cm / 1.6in border on all edges. Layer one-quarter of the romaine, tomato, red onion, and avocado slices across the sauce zone. Place one-quarter of the sliced chicken on top of the vegetables. Sprinkle 15g / 0.5oz of shredded cheddar over the chicken. Fold the left and right edges of the tortilla inward by 3cm / 1.2in, then roll the bottom edge up and over the filling, pulling firmly to keep the roll tight. Press the seam side down to hold the shape. Repeat with the remaining 3 tortillas.
