Wearing nitrile gloves, use a kitchen shears to gently cut the back shell of each lobster tail down to the tail fins.
Lift and separate the shell from the meat.
Rinse lobster meat; pat dry; chop or tear meat into large chunks; set aside.
Maine Style: In a large bowl, mix the celery, chives, lemon juice, lemon zest, salt, pepper and mayonnaise.
In a large saucepan over medium heat, melt half the butter; add lobster meat; cook, stirring continously ~2 minutes, until opaque and coated.
Butter and lightly toast insides of each brioche roll.
Connecticut Style: go to step 8; serve with melted butter. Maine Style: transfer lobster meat to mayonnaise mixture; toss to coat; chill.
Fill each roll with lobster meat; garnish with more chives, if desired.