Place the sweet potato on a baking sheet and bake until soft, 35 to 40 minutes. Allow to cool, then peel it.
Meanwhile, heat a large deep skillet over medium-high heat. Add the olive oil and heat until just hot. Add the carrots, celery, onion and salt. Cook, stirring occasionally, until the onions just turn translucent, about 5 minutes. Add the garlic, thyme and bay leaf and cook, stirring occasionally, until the vegetables are nice and brown, 5 to 7 minutes.
Stir in the tomatoes with their juices and cayenne, then stir in the broth. Bring to a boil, then reduce the heat to maintain a steady simmer until the carrots are tender, about 15 minutes. Remove and discard the thyme sprigs and bay leaf. Add the roasted sweet potato.
Using a blender, puree the soup until silky smooth. Return the soup to the skillet and heat on low. Stir in the cream. For a thinner soup, stir in more broth. Season to taste and serve hot with the micro basil and Croutons.
Pesto Grilled Cheese Croutons:
To the bowl of a food processor, add the basil, garlic, pine nuts, Parmesan, lemon zest and salt. Pulse until the mixture forms a chunky paste, scraping down the sides and bottom of the bowl occasionally. With the machine running, add the olive oil in a steady stream. Keep processing until the desired consistency is reached, pulsing less for a more coarse pesto and more for a smooth one. Season to taste.
To make the sandwiches: Spread some pesto on 1 side of 2 slices of bread. Arrange a slice of Cheddar over the pesto on 1 slice of bread. Sandwich with the other slice of the bread, pesto-side down. Repeat with remaining pesto, bread and Cheddar.
Mix the butter and mayo together in a small bowl. Spread a generous layer on both sides of each sandwich.
Place the sandwich in a nonstick skillet and turn the heat to medium-low. Cook, turning occasionally, until the bread is nice and toasty and golden brown, the cheese is melty and the sandwich is heated through. Repeat with the remaining sandwiches. Cut into croutons.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.