In a large heavy-bottomed pot, melt the ghee over medium heat until shimmering.
Add the diced onion, celery, and carrots to the pot and sauté for 5-7 minutes until the vegetables are softened and translucent.
Stir in the minced garlic and tomato paste, cooking for an additional 1-2 minutes until the paste turns a deep brick red and becomes fragrant.
Pour in the dry sherry to deglaze the pan, using a wooden spoon to scrape up any browned bits from the bottom.
Add the seafood stock, smoked paprika, sea salt, and black pepper, then bring the mixture to a gentle simmer for 10 minutes.
For a smooth texture, use an immersion blender to puree the soup until completely creamy, or leave it as is for a rustic style.
Lower the heat and stir in the full-fat coconut milk and the lobster meat, allowing it to heat through for 2-3 minutes without boiling.
Ladle the bisque into warm bowls and garnish with freshly chopped chives before serving.