How to Make It
Prepare the Lobster Stock: Cook lobster shells in hot oil in a large stockpot over high, stirring often, until bright red, about 10 to 15 minutes. Add onions, and cook, stirring often, until onions are translucent, about 6 minutes. Add garlic, star anise pods, lemongrass, ginger, and coriander seeds, and cook, stirring constantly, until fragrant, about 5 minutes. Add water, and cover. Reduce heat to medium, and cook 45 minutes. Pour mixture through a wire-mesh strainer into a large bowl, discarding solids. Set aside.
Marinate the Escabèche Vegetables and Fish: Pour orange juice, lime juice, and lemon juice through a wire-mesh strainer into a bowl, discarding seeds. Stir together sherry vinegar and combined juices. Toss fennel and shallot in juice mixture; cover and chill 1 hour.
Stir together orange zest, lime zest, lemon zest, salt and olive oil in a bowl. Add grouper; cover and chill 1 hour.
Meanwhile, prepare the Pepper Pot Soup: Heat oil in a Dutch oven over medium-high. Cook onions, ginger, habanero, lemongrass, and 2 teaspoons salt in hot oil, stirring occasionally, until vegetables begin to soften, about 4 minutes. Add squash, and cook, stirring occasionally, until almost soft, 6 minutes
Stir in Lobster Stock, coconut milk, and remaining 1 teaspoon salt; bring to a boil. Reduce heat to medium, and simmer, uncovered, until vegetables are tender, about 20 minutes. Remove and discard lemongrass. Process mixture with an immersion blender until smooth.
Prepare the Butternut Squash Topping: Toss together all Butternut Squash Topping ingredients in a small bowl; transfer to a small skillet. Cook over medium until golden brown and tender, about 5 minutes.
Prepare Escabèche Vegetables and Fish: Drain fennel mixture, discarding marinade and reserving vegetables. Remove grouper from marinade, discarding marinade. Season grouper with kosher salt and black pepper. Heat olive oil in a skillet over medium-high. Add grouper, and cook, stirring occasionally, until lightly browned and cooked through, about 2 minutes.
Assemble Caribbean Seafood Pepper Pot: Place 1/2 cup grouper strips in each of 4 soup bowls; spoon about 1 1/2 cups warm Pepper Pot Soup over grouper in each bowl. Top each with 2 tablespoons Escabèche Vegetables and 1/4 cup Butternut Squash Topping. Garnish each with reserved fennel fronds and chopped fresh basil, mint, and cilantro.