Combine the paprika, salt, garlic powder, thyme and cayenne, then toss the sirloin strips with the seasoning.
Stir the mayonnaise, Creole mustard and pickle brine together to make a thick remoulade.
Heat the neutral oil in a cast-iron skillet over high heat until shimmering.
Sear the steak in two batches for 2 to 3 minutes each, turning once, until the spice coating is dark red-brown and the beef reaches 145°F.
Spread the remoulade over the split rolls and divide the hot steak among them.
Top each sandwich with 1/2 cup shredded lettuce and close the rolls without crushing them.