In a large skillet, heat oil over low heat. Add carrot, onion, celery, and leek. Cook, until the vegetables are soft but not brown, 15 to 20 minutes. Add the sachet, and enough chicken stock to cover the vegetables. Bring to a boil, and reduce to a simmer, cooking until almost all of the liquid has evaporated, about 30 minutes.
Working in batches no larger than 2 cups, puree vegetables in a blender until very smooth. Let stand until cool. Measure 1/2 cup, and add carrot juice. Season with lime juice, salt, pepper, and Tabasco sauce. Reserve remaining puree for another use.