Step 1

In a large Dutch oven or other heavy-bottomed pot over medium-high heat, heat the olive oil until it shimmers. Add the onion and cook, stirring occasionally, until softened, about 3 minutes. Add the broccolini and garlic, and a big pinch each of salt and pepper. Cook, stirring occasionally, until the broccolini turns bright green and the thickest stems are fork-tender, about 5 minutes.

Step 2

Stir in the beans, broth and parmesan rind, if using. Increase the heat to high and bring the liquid to a boil. Reduce the heat to maintain a simmer, and cook, uncovered, until the broccolini is tender, 5 to 10 minutes. (It may lose its brightness or darken to an olive green; this is fine.)

Step 3

Remove the pot from the heat, fish out the parmesan rind if you used it, and stir in the cream, if using, a little at a time. While stirring, sprinkle the cheese into the soup. Using an immersion blender, puree the soup until it is as chunky or smooth as you’d like. (Or you can puree the soup in batches in a blender. Fill it no more than halfway, and be sure to remove the center ring from the lid and hold a kitchen towel over the lid as you blend to prevent splatters.) Taste, and season with more salt and pepper, as needed. Divide among bowls and serve, with additional parmesan on top, if desired.