Preheat your oven to 400°F. Peel and cut the carrot into chunks, drizzle with a little olive oil, and roast on a baking sheet for about 20 minutes until tender and lightly caramelized.
In a saucepan, heat 1 teaspoon of olive oil over medium heat. Sauté the chopped shallot and minced garlic until soft and fragrant, about 3-4 minutes.
Add the tomato paste to the saucepan and stir well, allowing it to cook for another 2 minutes to deepen the flavor.
Deglaze the pan with the dry white wine, scraping up any browned bits, and let it simmer for 2 minutes.
Pour in the low-sodium chicken broth and bring the mixture to a gentle simmer. Allow it to cook for about 5 minutes to let the flavors meld.
Add the roasted carrot to the saucepan and blend the bisque using an immersion blender until silky smooth. If you prefer a chunkier texture, blend only half of the mixture.
Gently stir in the light cream and add the fresh tarragon, reserving a few leaves for garnish.
Fold in the lobster meat carefully to warm it through without overcooking, about 2-3 minutes.
Taste and adjust seasoning with salt and pepper as needed. Ladle the bisque into bowls and garnish with the remaining fresh tarragon.
Serve immediately and enjoy the luxurious, silky texture with a hint of roasted sweetness and herbal freshness.