Heat a sauté pan or griddle to medium-high, spread the butter evenly on both side of the hot dog buns, and grill them until golden brown, about 2 minutes a side. Set aside the buns.
In a large bowl, mix the chopped lobster meat with mayo, mustard, roasted garlic, tarragon, parsley, celery, and scallions until everything is well incorporated. Season with the old bay and salt and pepper. Refrigerate the lobster salad for about an hour. Evenly distribute the lobster salad among the 12 grilled hot dog buns and serve.