Bring steaming water to a boil in a saucepan with a steamer basket. Add lobster tails, cover and steam for 10 to 12 minutes until the meat is opaque throughout and reaches 145°F.

Cool tails for 5 minutes, use kitchen shears to open the shells and remove all meat and shell fragments. Chop meat into small chunks and toss with the lobster butter, lemon juice and chopped tarragon.

Divide half the Fontina over 2 bread slices, add lobster evenly and top with remaining Fontina. Close with the other bread slices.

Butter the outside faces and cook in a large skillet over medium-low heat for 4 to 5 minutes per side until golden, Fontina is melted and the lobster filling is hot throughout.

Rest for 1 minute, cut each sandwich in half and serve immediately.