If lobster and shrimp are not already cooked: bring a large pot of salted water to a boil. Cook lobster tails for 8–10 minutes until opaque and firm; remove and cool, then remove meat and chop into bite-size pieces. Cook shrimp (medium) 2–3 minutes until pink; cool and chop. Pat shellfish dry on paper towels to remove excess moisture.

Mix dressing

In a medium bowl combine 1/2 cup mayonnaise, 1 tablespoon lemon juice, 1 teaspoon Dijon mustard, 1/2 teaspoon Old Bay seasoning, 1/2 teaspoon sea salt and 1/4 teaspoon freshly ground black pepper. Whisk until smooth and well blended. Taste and adjust salt, pepper or lemon as desired.

Combine filling

Add the chopped lobster (1 cup), chopped shrimp (1 cup), 1/4 cup finely diced celery, 2 tablespoons thinly sliced green onion, and 1 tablespoon chopped parsley to the dressing. Gently fold with a rubber spatula until the seafood is evenly coated, taking care not to break up the lobster pieces. Refrigerate the mixture for at least 15 minutes (or up to 2 hours) to let flavors meld.

Rolls & Finish

Toast buns

Heat a large skillet or griddle over medium heat. Spread about 3 tablespoons softened butter evenly across the cut sides of the 4 split-top buns. Add buns buttered-side down to the skillet and toast until golden brown and crisp, about 1–2 minutes. Remove and keep warm.

Assemble rolls

Divide the chilled lobster and shrimp mixture into 4 equal portions (about 1/2 cup per bun). Spoon each portion into a toasted bun, mounding slightly. Sprinkle each roll with a pinch more Old Bay or chopped chives/parsley if desired.

Serve

Serve immediately with lemon wedges on the side for squeezing over the filling. Optionally accompany with kettle chips or a simple green salad.