Melt the ghee in a large heavy-bottomed pot over medium heat.
Add the finely diced onion, carrot, and celery to the pot and sauté until the vegetables are softened and fragrant.
Stir in the minced garlic and tomato paste, cooking for about 1 minute until the paste darkens slightly.
Deglaze the pan with the dry sherry, using a wooden spoon to scrape up any browned bits from the bottom.
Pour in the seafood stock and add the fresh thyme, then bring the mixture to a gentle simmer for 10 minutes.
Carefully use an immersion blender to puree the soup base until it is completely smooth and uniform.
In a small bowl, whisk the arrowroot powder into the heavy cream until no lumps remain, then stir it into the soup.
Add the cooked lobster meat to the pot and simmer gently for 3-5 minutes until the lobster is heated through.
Season the bisque with sea salt and black pepper, then garnish with freshly chopped chives before serving.