Add the oil and heat until just hot. Add the carrot, celery, onion, and ½ teaspoon salt. Cook, stirring occasionally, until the onions just turn translucent, about 5 minutes.
Add the jalapeno, garlic, thyme, and basil. Cook, stirring occasionally, until the vegetables are nice and brown, about 7 minutes.
Stir in the tomatoes with their juices, then stir in the stock and sweet potato.
Bring to a boil, then reduce the heat to maintain a steady simmer. Simmer until the sweet potato is very, very tender, about 1 hour. The sweet potatoes should be soft enough to mash easily with the back of a spoon.
Remove and discard the thyme sprigs.
Using an immersion blender or stand blender (working in batches if necessary), puree until silky smooth.
Reheat the soup over low heat.
Stir in the cream.
For a thinner soup, stir in more stock.
Season to taste with salt and pepper and serve hot.