In a large heavy-bottomed pot, melt the ghee over medium heat until shimmering.
Add the finely diced yellow onion and celery, sautéing for 5-7 minutes until the vegetables are soft and translucent.
Stir in the minced garlic and tomato paste, cooking for another 2 minutes until the paste turns a deep brick red and becomes fragrant.
Pour in the dry sherry to deglaze the pot, using a wooden spoon to scrape up any flavorful browned bits from the bottom.
Add the seafood stock, sea salt, black pepper, and smoked paprika, then bring the mixture to a gentle simmer for 10 minutes to meld the flavors.
For a perfectly smooth texture, use an immersion blender to puree the soup base until it is completely creamy and uniform.
Lower the heat to low and stir in the full-fat coconut milk and the lobster meat, heating through for 3-4 minutes without allowing the soup to reach a boil.
Ladle the hot bisque into bowls and garnish with freshly chopped chives before serving immediately.