Heat the olive oil in a large Dutch oven over medium-high heat. Add the sausage, breaking it into crumbles, and cook 6–8 minutes until deeply browned in spots.
Push the sausage to one side and add the onion, carrot, and celery. Cook 5 minutes until softened, then add garlic and cook 30 seconds more.
Stir in the crushed tomatoes, chicken broth, and parmesan rind, scraping the bottom of the pot. Bring to a boil, then reduce to a low simmer.
Add the cannellini beans and simmer uncovered for 20 minutes, stirring occasionally.
Stir in the ditalini pasta and simmer 8–10 minutes until just al dente.
In the last 3 minutes, stir in the chopped kale in batches until wilted. Remove and discard the parmesan rind.
Season with salt, black pepper, and red pepper flakes to taste. Ladle into bowls and top with grated parmesan and a drizzle of olive oil.