Bring a pot of water to a boil and add kosher salt. Add the shrimp pieces and cook for just 1 to 2 minutes until they turn pink and opaque—don't overcook or they'll become rubbery. Drain the shrimp in a colander, rinse under cold water to stop the cooking, and pat dry thoroughly with paper towels. This moisture removal is crucial for a properly textured salad. Toss the cooked shrimp with 3/4 tsp Old Bay seasoning and 1 tsp lemon juice, then transfer to a bowl and refrigerate for at least 20 minutes to chill and let the flavors meld.
While the shrimp chills, prep your vegetables for maximum crunch and flavor distribution. Dice the celery ribs into small 1/4-inch pieces—this size ensures even distribution throughout the salad and prevents large, watery bites. Finely chop the fresh dill and dice the scallions, keeping them separate for now. I like to prep the celery first since it takes the most knife work, then move to the more delicate herbs and alliums.
In a small bowl, whisk together the mayonnaise, remaining 1 1/4 tsp Old Bay seasoning, 2 tsp fresh lemon juice, Worcestershire sauce, and Dijon mustard. The Worcestershire and mustard add depth and umami without overpowering the delicate shrimp. Taste as you go—I find the fresh lemon juice brightens the whole mixture and prevents it from tasting too heavy.
Remove the chilled shrimp from the refrigerator and add the diced celery, chopped dill, and scallions to the bowl. Pour the dressing over the shrimp and vegetables, then fold everything together gently until evenly coated—avoid aggressive stirring so the shrimp pieces stay intact. Taste and adjust seasoning if needed. The salad can be served immediately or chilled further for up to 2 hours before assembly.
Split the Hawaiian rolls and lightly toast them if desired for a bit of texture (this also prevents the bread from getting soggy). Place a small handful of shredded lettuce on the bottom half of each roll to create a barrier between the bread and the moist shrimp salad. Divide the shrimp salad evenly between the rolls, top with the other half, and serve immediately. The lettuce helps keep the sandwich structurally sound and adds a fresh, crisp element.