Prepare Dressing: In a mixing bowl, combine ⅓ cup mayonnaise, 1 tablespoon finely chopped green onion, 1 teaspoon Dijon mustard, and the juice and zest of 1 lemon. Season with ½ teaspoon kosher salt and ¼ teaspoon black pepper, stirring until smooth and creamy. Reserve a couple of tablespoons for later.

Grill Shrimp: Preheat grill to high heat (around 400°F/204°C). Skewer the raw large shrimp, coating them with remaining dressing. Grill for approximately 2 minutes per side until opaque, then cool slightly.

Make Shrimp Salad: Chop grilled shrimp into bite-sized pieces. In a clean bowl, mix chopped shrimp with reserved dressing, ½ cup finely chopped celery, and ¼ cup fresh parsley. Stir gently to combine.

Toast Rolls: Spread softened butter on the outsides of hot dog rolls. Preheat a skillet over medium heat and toast rolls until golden brown and crispy on both sides (2-3 minutes).

Assemble Rolls: Fill toasted rolls with the shrimp salad, allowing it to overflow slightly. Serve with crispy potato chips or tangy pickles.