Pat the lobster tails completely dry with a paper towel. Heat a large skillet over medium heat and add the olive oil and butter. Add the lobster tails and cook until they are just opaque and pink, about 5 to 6 minutes, tossing once during cook time. Remove the lobster tails and place them on a plate. You can chop them up a bit to fit more easily in the sandwiches!
Keep the same skillet over medium heat. Spread the insides of each piece of bread with mayo. Spread the outsides with the tarragon garlic butter. Place the cheese and lobster on the inside of each bread slice – I like to make sure there is cheese on both sides to act like “glue” and hold the sandwich together!
Toast over medium heat until golden on both sides and the cheese is melty – about 4 to 5 minutes per side. Serve immediately!
tarragon garlic butter
Stir together the ingredients in a bowl until combined. Any extra stays great in the fridge in a sealed container!