Lobster and Macaroni Gratin

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2 tablespoons unsalted butter

4 pounds lobster, claw and tail meat removed, and set aside, discard the shell and reserve the coral and tomalley

1/4 cup Cognac

1/4 cup small diced carrot

2 tablespoons small diced celery

3 tablespoons minced shallots

1 teaspoon minced garlic

2 tablespoons finely chopped parsley

1/2 cup port wine

1 bouquet garni

3 cups plus 2 tablespoons creme fraiche

7 ounces tiny macaroni, cooked al denta and tossed with olive oil

1 egg yolk

3 tablespoons shredded Gruyere cheese, plus 1 tablespoon

Salt and pepper

2 cooked whole lobster claws

Long chives

1 tablespoon chopped chives