Bring a large sauce pot full of salted water to a boil. Place lobsters into it, two at a time, head first. Cook for about 8 minutes from the time they enter the water. Transfer with tongs to an ice bath and cool. Return water to a boil and cook and cool the remaining lobsters.
Set lobsters on a cutting board and start with the tail when removing meat from the shells. Remove all meat from tail, claws and joints. (Pro tip: save carcasses to make a lobster stock.)
Coarsely chop the meat.
In a large bowl, whisk together the vinaigrette ingredients.
Add lobster and gently toss, season with sea salt.
Brush the inside of the buns with butter. Grill, buttered side down until golden.
Fill the buns with lobster salad, sprinkle with chives and enjoy!