If cooking raw shrimp, bring a large pot of salted water to a gentle boil. Add the shrimp and cook for 2-3 minutes, or until pink and opaque. Immediately transfer to an ice bath to stop the cooking. Drain well, pat dry, and chop into bite-sized pieces.
In a large bowl, whisk together the mayonnaise (or mayonnaise and Greek yogurt), Dijon mustard, lemon zest, lemon juice, Old Bay seasoning, salt, and pepper.
Fold in the chopped shrimp, celery, red onion, dill, and chives until everything is evenly coated.
Cover and refrigerate for at least 30 minutes to allow the flavors to develop.
Butter the brioche buns and toast them in a skillet until golden brown.
Add butter lettuce to each bun and generously pile on the chilled shrimp salad.
Garnish with extra dill, cracked black pepper, and an extra sprinkle of Old Bay if desired.