Slice each chicken breast in half lengthwise to make 4 thin cutlets. Pat all pieces dry with paper towels.

Evenly coat both sides of the 4 cutlets with 3–4 tablespoons blackened seasoning, pressing gently so the seasoning adheres.

Heat a skillet over medium-high heat. Add 1 tablespoon olive oil and 2 tablespoons butter and heat until the butter is melted and the fat is hot and beginning to sizzle.

Add the seasoned cutlets to the hot skillet in a single layer without crowding (cook in batches if needed). Cook until a dark crust forms and the first side is browned, about 4–6 minutes.

Flip the cutlets and cook the second side until the chicken reaches 165°F (74°C) in the thickest part, about 4–6 minutes more.

Transfer the cooked chicken to a plate and let rest for 4–5 minutes before slicing or serving.