In a small bowl, mix together the paprika, cayenne, garlic powder, thyme, salt, and black pepper. Pat the chicken breasts completely dry with paper towels - this is crucial for the spice to adhere and the meat to sear properly. Rub the spice mixture all over both sides of the chicken, pressing it in so it sticks.

Open a window or turn on your exhaust fan - this will smoke. Heat the vegetable oil in a cast iron skillet over medium-high heat until it shimmers and just barely starts to smoke, about 3 minutes. Add the chicken and cook without moving it for 5-6 minutes until the bottom is deeply browned and nearly black in spots. Flip and cook another 4-5 minutes until the internal temperature reaches 165F. Transfer to a cutting board and let rest for 5 minutes.

While the chicken rests, whisk the buttermilk, mayonnaise, lemon juice, and hot sauce (if using) in a small bowl until smooth. Season with a pinch of salt.

In a large bowl, combine the chopped romaine, cherry tomatoes, cucumber, and red onion. Drizzle with about half the dressing and toss to coat lightly - you can always add more, but you cannot take it away.

Slice the rested chicken against the grain into half-inch strips. Arrange over the dressed salad and drizzle with remaining dressing, or serve it on the side. Serve immediately while the chicken is still warm.