Soak chicken in buttermilk for at least 15 minutes, up to 2 hours in the fridge.
Whisk together flour, smoked paprika, garlic powder, salt, and pepper in a shallow dish.
Dredge chicken in the flour mixture, pressing firmly to coat.
Heat oil in a large skillet over medium heat until shimmering.
Cook chicken for 4 to 5 minutes per side until golden and cooked through to 165F.
Rest chicken on a wire rack for 2 minutes.
Spread caesar dressing on toasted rolls, then layer with romaine, chicken, and parmesan before serving.