To prepare the burger patties, divide the beef into 4 equal size portions. Shape into 1/2 inch thick patties. Do not overwork the beef or your burger will be dense and dry.
Press your thumb into the center of each patty, leaving an indent the size of a nickel. This will help the patty hold its shape. (Tip from Cooking Light magazine)
Sprinkle the burger patties with 1/2 tsp. kosher salt and 1/2 tsp. Old Bay Seasoning. Set aside.
Cut each shrimp into 2-3 pieces. In a medium bowl, combine shrimp, onions, celery, tarragon, mayo, remaining 1/2 tsp. salt and 1/2 tsp. Old Bay Seasoning, 1/2 tsp. black pepper and the lemon juice. Mix until well combined.
Preheat grill to medium-high heat.
Place the prepared burger patties on the grill. Grill to your liking. I grilled mine for 4 minutes per side for medium burgers. Top with cheese during last minute if desired.
Remove from grill and let stand for about 5 minutes.
Toast the buns while burgers are resting.
Place lettuce and tomato on top of bottom bun, top with burger, then a nice scoop of shrimp salad.