Season the chicken strips with salt, pepper, smoked paprika, Italian seasoning, and garlic powder. Let sit at room temperature for about 10–15 minutes.
Warm 1–2 tablespoons olive oil in a large skillet over medium heat. Add the minced garlic and cook just until fragrant, about 30 seconds, stirring constantly.
Add the seasoned chicken strips to the skillet and cook for 6–8 minutes, stirring occasionally, until the chicken is no longer pink and lightly golden in spots.
In a small bowl, mix the Greek yogurt or sour cream with a pinch of salt and pepper. Once the chicken is cooked, reduce the heat to low and stir in the yogurt or sour cream mixture until the chicken is evenly coated.
Sprinkle in the mozzarella and cheddar cheeses and cook for another 1–2 minutes, stirring gently, until the cheese melts and the filling is creamy.
Remove the skillet from the heat and stir in the chopped parsley or cilantro. If using, add shredded lettuce or spinach and toss just until slightly wilted.
Warm each low‑carb tortilla in a dry skillet or in the microwave for 10–15 seconds so it becomes pliable but not soggy.
Place a warm tortilla on your work surface, spoon a generous portion of the cheesy garlic chicken filling in the center, fold in the sides, then roll it up tightly from the bottom.
Carefully return each filled wrap to the skillet over medium heat and cook for 2–3 minutes per side, until the tortilla is lightly golden and any cheese along the edges starts to crisp.
Slice each wrap in half diagonally and serve warm, drizzling with garlic aioli or ranch‑style sauce if desired.