In a 5-quart pot, melt the butter over medium-high heat.
Add the onion, carrots, and celery. Cook, stirring only occasionally, until softened and well-browned in spots. Don't rush this step — the browning adds lots of good flavor to the soup.
Add the garlic, give it a stir, and cook for a minute.
Sprinkle in the flour, stir to coat the vegetables, and cook for a minute more.
Stir in the tomato paste and cook for one additional minute.
Pour in the wine and give it an aggressive stir, scraping up the browned bits on the bottom of the pot. The mixture will start to thicken immediately. Simmer briskly for one minute.
Pour in the lobster stock. Add the tarragon sprig and the bay leaf and give it a stir.
Bring to a boil, then simmer, uncovered for 10 minutes.
Stir in the heavy cream, salt (if using), pepper, and cayenne, and simmer five minutes more.
Remove tarragon sprig and bay leaf. Carefully transfer the entire remaining contents of the pot to a blender and puree until perfectly smooth. I love my Vitamix for creating beautifully silky results, but a regular blender is just fine. Alternatively, use an immersion blender.
Wipe out the pot and pour the pureed soup back in.
Stir in the lobster meat and taste for seasoning.
Ladle into serving bowls and garnish with snipped chives.