Fill a large stockpot 3/4 full with salted water and bring to a boil. Plunge the lobsters headfirst into the boiling water and blanch for 3 minutes. Transfer tongs to a large bowl filled with ice water to cool.
When the lobsters are cool enough to handle, crack the shells and remove the meat from the tail if using a spiny lobster, and from the tail and claws if using a Maine lobster. Cut into bite-sized pieces and set aside.
Preheat a grill to medium-high. (Or preheat the oven to 375 degrees F.)
Combine the oil and Essence in a small bowl, and lightly rub both sides of each fillet with the mixture.
Place the fish, flesh side-down on the grill and cook for 2 minutes. Turn the fillets 1/4 turn to make decorative grill marks and cook an additional 2 minutes. Turn and cook skin side-down until the fish flakes easily, about 4 minutes. (Alternatively, place the seasoned fish on a nonstick baking sheet and roast until golden brown and cooked through, 10 to 12 minutes.)
Place the fish on a large platter.
In a large skillet or saute pan, melt the butter over medium-high heat. Add the shallots and garlic and cook, stirring, until soft, about 1 minute. Add the wine, lemon juice, capers, salt, and cayenne and simmer for 2 minutes. Fold in the chopped lobster, stir to combine, and cook until heated through, about 1 minute. Remove from the heat, stir in the parsley, and adjust the seasoning to taste.
Top the fish with the sauteed lobster. Garnish with lemon supremes and chopped chives.
Yield: 4 servings