
Hot Italian sausage complements the sweet potatoes and greens, providing just the right amount of heat in this comforting soup. Simmering with rosemary sprigs infuses the soup with aromatic flavor without the extra work required to mince the leaves before cooking them.
Heat oil in large heavy pot over medium-high heat. Add sausage; cook, stirring to crumble, until browned, 6 to 8 minutes. Transfer the sausage to a clean plate. Add onion, celery, and garlic to the pot; cook, stirring often, until softened, 3 to 4 minutes. Return the sausage and any accumulated juices to the pan.
Stir in 1 cup broth, scraping the bottom of the pot to loosen browned bits. Stir in sweet potatoes, tomatoes, the remaining 4 cups broth, pepper, and salt. If using fresh rosemary, tie the sprigs together with butcher's twine or secure in a cheesecloth bag. Add the rosemary bundle to the stew, gently pressing into the liquid (or sprinkle in the dried rosemary). Bring to a boil. Reduce to heat to low; simmer, uncovered, until the sweet potatoes are fork-tender, 15 to 20 minutes. Discard the rosemary sprigs, if using.
Stir in kale; cook until wilted, 1 to 2 minutes. Top each serving with Parmesan.