Mix softened butter with 1 teaspoon of freshly chopped tarragon.
Preheat a pan over medium-low heat. Spread mayo on one side of your bread, and tarragon butter on the other. Place butter side down in your frying pan. Add cheese slices on top of the bread.
Place Diced Lobster on top of your cheese layer.
Top with a second layer of cheese and 1/2 teaspoon of fresh chopped tarragon. Since this grilled cheese is thick, cooking it on medium-low heat is important. You want the cheese to melt, but you don’t want to burn your bread. Place a lid over the pan and watch carefully.
When your cheese starts melting, apply mayo and butter to your second slice of bread, place on top, then carefully flip. Place the lid back on and allow the second side to toast.