Dry the thawed lobster meat using paper towels and chop into smaller pieces if desired.
Melt 2 tablespoons of butter in a skillet over medium heat and add the lobster meat along with the minced garlic. Cook while stirring gently until the lobster is heated through and coated in butter, about 2 to 3 minutes.
Transfer the lobster meat to a mixing bowl and mix in the chopped chives, lemon zest, lemon juice, Creole Cajun seasoning, and freshly ground black pepper. Toss lightly to combine. Clean the skillet by discarding the leftover butter.
Heat 2 to 3 tablespoons of butter in the cleaned skillet over medium heat. Brush the butter onto the sides of each brioche bun. Toast the buns in the skillet until golden and crisp on all sides, then wipe the skillet clean again.
Lower the stove heat and melt the remaining butter in the skillet, then pour this melted butter over the seasoned lobster meat and toss to coat well.
Spread mayonnaise inside each toasted bun and fill evenly with the warm lobster mixture. Garnish with extra chopped chives if you like. Serve right away with lemon wedges and your choice of chips or sides. Enjoy!