Heat a grill or grill pan to medium heat.
Brush the fillets with the olive oil and sprinkle on all sides with the fish rub. When the grill is hot, place the fillets evenly spaced on the grill. Cook until the fish is just cooked through, about 5 minutes per side. Flip only once if possible.
While the fish is cooking, combine the mayonnaise, cilantro, relish, garlic and a sprinkle of salt and pepper in a medium bowl. Start with a generous tablespoon of hot sauce, then stir and taste to assess the heat. If more is preferred, add up to 1 more tablespoon. Set aside.
Slice the buns and place face-down on the grill until toasted, or toast in the oven. Spread the desired amount of the tartar sauce, around 2 tablespoons, on the top half of each bun. Place the grilled fish on the bottom halves.
If desired, quickly grill the romaine leaves until some light charring occurs. Top each sandwich with 1 leaf and enjoy!
Steak-like fish, such as amberjack or mahi, indicate their doneness as the sides turn white. Once the sides are white a little over halfway, flip the fish.
Recipe courtesy of Emeril Lagasse, copyright MSLO Inc., all rights reserved