Pat the chicken cutlets dry with paper towels—this is crucial for getting a good sear and helping the seasoning adhere properly. Lightly brush both sides of each cutlet with avocado oil, then generously coat both sides with the Cajun seasoning mixed with dried thyme. I like to press the seasoning gently into the meat so it creates a flavorful crust rather than just sitting on the surface. Let the seasoned cutlets sit at room temperature for 5-10 minutes while you prepare your skillet.
Heat the remaining avocado oil and butter together in a large skillet over medium-high heat until the butter is foaming and the oil shimmers (about 1-2 minutes). Working in batches if needed to avoid overcrowding, carefully lay the seasoned chicken cutlets into the hot skillet. Sear for 2-3 minutes per side without moving them—the first side is where the blackened crust develops, so resist the urge to flip early. The chicken is done when the internal temperature reaches 165°F and the seasoning has created a dark, caramelized crust.
Transfer the cooked chicken to a plate and let it rest for 3-5 minutes before serving. I find this resting period allows the juices to redistribute, keeping the meat tender and moist rather than dry.