Pound the chicken breasts between plastic wrap to an even ¾-inch thickness. Pat completely dry with paper towels.
Mix the paprika, cayenne, garlic powder, onion powder, thyme, oregano, salt, and pepper in a small bowl. Press the spice blend evenly onto both sides of the chicken.
Heat the olive oil in a cast iron or heavy stainless skillet over high heat until it shimmers and just starts to smoke, about 2–3 minutes.
Sear the chicken for 4 minutes per side without moving it, until a dark crust forms and the internal temperature reaches 160°F.
Transfer the chicken to a cutting board and rest for 5 minutes.
Whisk together the mayonnaise, minced garlic, lemon juice, minced anchovy, Worcestershire sauce, and grated parmesan in a large bowl to make the dressing.
Add the chopped romaine to the bowl and toss until evenly coated.
Slice the rested chicken against the grain into strips.
Divide the dressed romaine among plates, top with sliced chicken, shaved parmesan, and croutons. Serve immediately.