In a large heavy-bottomed pot, melt the ghee over medium heat.
Add the finely diced onion, celery, and carrot, sautéing for about 5-7 minutes until the vegetables are soft and translucent.
Stir in the tomato paste and cook for 2 minutes to deepen the flavor profile.
Pour in the dry sherry to deglaze the pot, scraping up any browned bits from the bottom.
Add the seafood stock, sea salt, and black pepper, then bring the mixture to a gentle simmer for 10 minutes.
Using an immersion blender, puree the soup base until completely smooth and uniform.
In a small bowl, whisk the arrowroot powder with a tablespoon of water to create a slurry, then stir it into the simmering soup to thicken.
Reduce heat to low and stir in the full-fat coconut milk and the lobster meat, heating through for 3-4 minutes without boiling.
Ladle the bisque into bowls and garnish with freshly minced chives before serving.