Melt the ghee in a large pot over medium heat, then add the minced shallots, carrots, and celery.
Sauté the vegetables for 5 to 7 minutes until softened and fragrant.
Stir in the minced garlic and tomato paste, cooking for 1 minute to deepen the color and flavor.
Pour in the dry sherry to deglaze the pot, scraping up any browned bits from the bottom.
Add the seafood stock, dried thyme, bay leaf, and smoked paprika, then bring the mixture to a gentle simmer.
Reduce heat to low and let the broth simmer for 15 minutes to allow the flavors to meld.
Remove the bay leaf and use an immersion blender to puree the soup until it reaches a smooth, velvety consistency.
Stir in the full-fat coconut milk and the cooked lobster meat, heating through for 3 to 5 minutes.
Season with sea salt and black pepper before serving hot in a shallow bowl.