Heat a cast-iron skillet over high heat for 10 minutes until white-hot. While the skillet is heating up, toast the brioche buns and set them aside.
Brush chicken breasts with butter, then coat with blackening seasoning on all sides. Add the remaining butter to the hot skillet. Add the chicken on top of the butter. Cook the chicken for 3 minutes without moving, then flip and cook for another two minutes on the other side. Remove from the heat and set aside.
Add a slice of provolone cheese to each piece of chicken, then microwave for about 30 seconds to melt the cheese.
Salt the tomato slices. Add 1 tbsp Spicy Aioli to each bread half. Add a chicken cutlet, a tomato slice, and a lettuce leaf to build the sandwich.
Complete the sandwich, then cut it in half to serve.