Roughly chop the shrimp. In a pan, melt butter and cook the shrimp over medium-low heat for about 2 minutes. Remove from heat and let the shrimp cool completely.
In a medium bowl, mix mayo, lemon juice, lemon zest, dill, chives, and garlic.
Add the shrimp, celery, red onion, salt, pepper, and Old Bay seasoning. Mix until combined. Chill shrimp salad for at least 20 minutes.
Cut a small slice out of the center of each roll, so there’s more space for shrimp. Lightly toast the buns. Brush melted butter inside the buns and fill with the shrimp salad.