Set an oven rack about 6 inches from the heat and turn on the broiler. Put a sheet pan on the counter so it is ready for the broccoli.

Put the broccoli on the sheet pan. Drizzle it with 1 tablespoon of the olive oil, sprinkle with 1/2 teaspoon of the salt and 1/4 teaspoon of the black pepper, and toss until coated.

Spread the broccoli into one layer on the sheet pan. Broil for 8 to 10 minutes, stirring once halfway through, until the edges are dark in spots and the stems are tender.

While the broccoli cooks, set a large soup pot on the stove over medium heat. Add the remaining 1 tablespoon olive oil.

Add the onion to the pot. Cook for 4 to 5 minutes, stirring often, until it softens and starts to turn light golden at the edges.

Add the garlic to the pot. Cook for 30 seconds to 1 minute, stirring, until it smells fragrant but does not brown.

Put the drained beans into the pot. Stir for about 30 seconds so they warm through and pick up the onion and garlic flavor.

Pour 4 cups of the vegetable broth into the pot. Raise the heat to high and bring the broth to a gentle boil.

Transfer the broiled broccoli from the sheet pan into the pot. Make sure to scrape in any browned bits from the pan.

Lower the heat to medium-low and simmer the soup for 5 minutes so the broccoli softens a little more and the flavors come together.

Use an immersion blender, which is a hand blender that works right in the pot, and blend the soup for 10 to 15 seconds. Stop while the soup is still chunky; you only want some of the beans and broccoli to break down and lightly thicken the broth. If you do not have an immersion blender, mash some of the beans and broc…

Pour the remaining 2 cups broth into the pot. Turn the heat back up to high and bring the soup to a full boil.