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Preheat oven to 350°F. Build of living garlic, lower aspect up, on an 8-jog square of aluminum foil. Drizzle with 1 1/2 teaspoons oil and wrap in foil to seal. Roast till very relaxed, about 1 hour and Half-hour. Unwrap and let cool totally. Squeeze garlic cloves correct into a runt bowl; discard peels. Field apart.
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Soften 1/2 cup butter in a runt saucepan over medium-low. Cook, stirring once shortly, till foamy, about 4 minutes. Continue to cook, stirring often, till milk solids flip golden brown and butter smells nutty, about 4 minutes. Transfer brown butter to a runt bowl; space apart.
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Bring lobster inventory to a boil over medium-high. Lower warmth to medium-low and simmer, uncovered, till reduced to 1 quart, about 50 minutes. Add 1/3 cup Cognac; cook till combination has reduced to 1 quart, about 5 minutes. Add cream, brown butter, and piment d’Espelette; plug to mix. Alter warmth to care for a delicately simmer. Cook, stirring once shortly, till combination coats the back of a spoon and has reduced to 1 quart, about 1 hour and Half-hour. Slip in lemon juice, 1/2 teaspoon salt, and just a few grates of nutmeg. Veil and care for warmth over low.
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Build of living pike and scallops in a medium bowl. Freeze till very frigid, about quarter-hour. Transfer to a meals processor, and course of till very finely chopped, about 10 seconds. Add egg yolks, egg, softened butter, 1 tablespoon salt and a pair of teaspoons roasted garlic. (Reserve very best garlic for one other employ.) Course of till combination is awfully relaxed, about 1 minute and 30 seconds (fabricate now not let combination receive warmth). Add crème fraîche and pulse till included, about 10 times.
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Like a pleasing Dutch oven with water to a depth of three inches. Warmth over low to 170°F. Shape pike combination into 16 ovals (about 1/4 cup every) by the employ of a spoon to press and relaxed combination in opposition to a 2d spoon. Cook quenelles, in batches if most necessary, in water, flipping and bobbing to submerge once shortly, till cooked thru, about quarter-hour, adjusting warmth as wished to care for 170°F.
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Warmth very best 1 1/2 tablespoons oil in a pleasing skillet over medium-high. Add mushrooms; cook, stirring once shortly, till evenly browned and relaxed, 6 to eight minutes. Sprinkle with very best 1/4 teaspoon salt and space apart.
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Preheat broiler to high with oven rack 6 inches from warmth. Build of living 2 quenelles in every of 8 (12-ounce) gratin dishes and spoon 1/2 cup lobster sauce into every dish over quenelles. Build of living gratin dishes on a rimmed baking sheet and broil till sauce begins to bubble and evenly brown, 2 to 4 minutes. Field sizzling gratin dishes on serving plates.
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Divide mushrooms and crayfish tails evenly among gratin dishes. Sprinkle every dish with 1/4 teaspoon cognac. Prime every with 1 entire crawfish and garnish with parsley.
Notes
Acquire the Lobster Stock recipe here
