Step 1

Heat a large Dutch oven or pot over medium-high heat. Add the sausage and break it up into small pieces with a wooden spoon, making sure the pieces sit in a single layer (if they don't, remove some and work in batches). Cook, stirring several times, until no longer pink on the outside and golden brown in places, about 10 minutes. Transfer to a plate with a slotted spoon.

Step 2

Add the onions to the pot. If there are lots of browned bits on the bottom that look like they might burn, add 2 tablespoons of broth and scrape the bottom with a wooden spoon. Cook the onions, stirring frequently and adding more broth to the bottom of the pot as needed, until completely tender, about 10 minutes. Add the white beans and remaining broth and bring to a boil. Reduce to a simmer and cook over medium heat until the beans split open, about 10 minutes.

Step 3

Use an immersion blender to puree the soup in the pot until completely smooth or carefully transfer the hot liquid to a blender to puree. Season the soup with salt. Serve the soup topped with the sausage.