Steam or boil live lobster until cooked through. Remove lobster meat and reserve. Reserve shells for stock.
Make lobster stock by simmering lobster shells in 6 cups of water with aromatics (onion, carrot, celery, bay leaf) for 1.5 hours. Strain and reserve.
In a large pot, melt Clarified butter from Aromatics group over medium heat. Add Shallots and Garlic and cook until softened, about 5 minutes.
Add Lobster stock from Liquids group and bring to a simmer. Reduce heat and simmer for 20 minutes.
In a small bowl, whisk together Cornstarch and Cold water from Thickening group to create a slurry. Gradually whisk the slurry into the simmering bisque, stirring until thickened.
Stir in Heavy cream and Cognac from Liquids group. Heat through, but do not boil.
Add Lobster meat, Old Bay seasoning, Salt, White pepper, and Tarragon from Seasoning group. Cook for 2-3 minutes, until heated through.
Serve hot, drizzled with Chive oil from Garnish group.
