In a small saucepan, bring 1 1/2 cups stock and the sun-dried tomatoes to a low boil. Lower the heat and simmer until softened, 6-7 minutes.
Meanwhile, in a large saucepan, heat the EVOO, 2 turns of the pan, over medium-high heat. Add the onion, carrot, garlic, bay leaf and thyme; season with salt and pepper. Cook until the veggies are softened, about 5 minutes. Stir in the vodka; deglaze and reduce for a minute. Add the crushed tomatoes and reduce to thicken a bit, 15-18 minutes. Add the remaining 2 1/2 cups stock, the reconstituted sun-dried tomatoes and their stock, and the basil. Puree with an immersion blender, return to a bubble and stir in the cream.