Bring a pot of water to a boil, 3 or 4 inches deep. Add lobster tails to the water and boil 7 to 8 minutes. Drain and shock under cold water to cool. Use kitchen scissors to cut away soft underside of tails. Remove meat and save the shells, arranging them in a shallow casserole dish. Chop the cooked meat on an angle into chunks.
Preheat your broiler to high.
Heat a medium skillet and a small saucepot over medium heat. To the small saucepot, melt 2 tablespoons butter. Add finely chopped onion and cook 3 to 5 minutes until very soft. To the skillet, add remaining 2 tablespoons butter. When the butter melts, add chopped lobster meat and saute.
Add flour to sauce pot with onions and cook together another 1 to 2 minutes. Whisk in wine or sherry, then milk. Remove sauce from heat and stir in cheddar cheese and paprika or crab boil. Season sauce with salt and pepper. Pour sauce over lobster meat and stir to combine. Pour lobster into and over the shells in a casserole dish and top with Parmesan and bread crumbs. Broil on high until golden, 2 or 3 minutes. Serve each tail, spilling over with lobster bits in sauce, on a bed of mixed baby greens and parsley with wedges of lemon along side.
To make this dish with jumbo shrimp, cut up peeled, deveined raw shrimp. Saute the shrimp in butter, as with cooked lobster. Cook until pink and firm and proceed with method. Place the shrimp and sauce into a small casserole, then spoon completed shrimp Thermidor over bed of greens and parsley leaves.
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