How to Make It
Preheat oven to 350°F. Place garlic, cut side up, on an 8-inch square of aluminum foil. Drizzle with 1 1/2 teaspoons oil and wrap in foil to seal. Roast until very soft, about 1 hour and 30 minutes. Unwrap and let cool completely. Squeeze garlic cloves into a small bowl; discard peels. Set aside.
Melt 1/2 cup butter in a small saucepan over medium-low. Cook, stirring occasionally, until foamy, about 4 minutes. Continue to cook, stirring often, until milk solids turn golden brown and butter smells nutty, about 4 minutes. Transfer brown butter to a small bowl; set aside.
Bring lobster stock to a boil over medium-high. Reduce heat to medium-low and simmer, uncovered, until reduced to 1 quart, about 50 minutes. Add 1/3 cup Cognac; cook until mixture has reduced to 1 quart, about 5 minutes. Add cream, brown butter, and piment d’Espelette; stir to combine. Adjust heat to maintain a gently simmer. Cook, stirring occasionally, until mixture coats the back of a spoon and has reduced to 1 quart, about 1 hour and 30 minutes. Stir in lemon juice, 1/2 teaspoon salt, and a few grates of nutmeg. Cover and keep warm over low.
Place pike and scallops in a medium bowl. Freeze until very cold, about 15 minutes. Transfer to a food processor, and process until very finely chopped, about 10 seconds. Add egg yolks, egg, softened butter, 1 tablespoon salt and 2 teaspoons roasted garlic. (Reserve remaining garlic for another use.) Process until mixture is very smooth, about 1 minute and 30 seconds (do not let mixture get warm). Add crème fraîche and pulse until incorporated, about 10 times.
Fill a large Dutch oven with water to a depth of 3 inches. Heat over low to 170°F. Shape pike mixture into 16 ovals (about 1/4 cup each) by using a spoon to press and smooth mixture against a second spoon. Cook quenelles, in batches if necessary, in water, flipping and bobbing to submerge occasionally, until cooked through, about 15 minutes, adjusting heat as needed to maintain 170°F.
Heat remaining 1 1/2 tablespoons oil in a large skillet over medium-high. Add mushrooms; cook, stirring occasionally, until lightly browned and tender, 6 to 8 minutes. Sprinkle with remaining 1/4 teaspoon salt and set aside.
Preheat broiler to high with oven rack 6 inches from heat. Place 2 quenelles in each of 8 (12-ounce) gratin dishes and spoon 1/2 cup lobster sauce into each dish over quenelles. Place gratin dishes on a rimmed baking sheet and broil until sauce begins to bubble and lightly brown, 2 to 4 minutes. Set hot gratin dishes on serving plates.
Divide mushrooms and crayfish tails evenly among gratin dishes. Sprinkle each dish with 1/4 teaspoon cognac. Top each with 1 whole crawfish and garnish with parsley.
Get the Lobster Stock recipe here