Bring a medium pot of salted water to a gentle boil. Add the shrimp and cook until just opaque and pink, 2–3 minutes depending on size. Do not overcook. Drain and immediately transfer shrimp to an ice bath to stop cooking. Once cool, pat shrimp dry and chop into 1/2-inch pieces.

Mix dressing

In a medium bowl combine mayonnaise, lemon juice, Dijon mustard, chopped dill/parsley, Old Bay (or seafood seasoning), salt, and pepper. Whisk until smooth and taste; adjust seasoning with extra lemon or salt if needed.

Combine filling

Add the chopped shrimp, diced celery, and sliced green onion to the dressing. Fold gently until everything is evenly coated. Refrigerate the filling for at least 15 minutes to meld flavors (up to 2 hours).

Prepare Rolls and Assemble

Toast rolls

Preheat a skillet or griddle over medium heat. Spread a thin layer of softened butter on the cut sides of each roll. Place rolls buttered-side down in the skillet and toast until golden and crisp, about 2 minutes. Remove from heat.

Line with lettuce

Place a lettuce leaf inside each toasted roll to create a barrier that keeps the roll from becoming soggy and adds a fresh crunch.

Fill rolls

Divide the chilled shrimp mixture evenly among the 4 rolls (approximately 3 shrimp each, with dressing and veggies). Mound the filling lightly so the roll is generously filled but not overflowing.

Garnish and serve

Sprinkle each roll with chopped chives and add a small lemon wedge on the plate. Serve immediately with cocktail sauce or remoulade on the side for dipping.

Make-Ahead & Serving Notes

The shrimp mixture can be made up to 2 hours ahead and kept covered in the refrigerator. Toast rolls just before serving for best texture. If using pre-cooked shrimp from the store, reduce resting time; still chop and toss with the dressing before assembling.