Step 1

Arrange a rack in the middle of the oven and heat the oven to 450ºF.

Step 2

Trim off any brown or dry areas from the stem end of 2 small or 1 large broccoli crown. Cut the crown into large florets. Chop the stem crosswise (if you have any left) into 1-inch chunks. Place the broccoli on a rimmed baking sheet. Drizzle with 1 tablespoon of the olive oil, sprinkle with 1/4 teaspoon of the kosher salt, and toss to coat. Spread out in a single layer.

Step 3

Place 6 large unpeeled garlic cloves in the center of a 6-inch square of aluminum foil. Drizzle with 1/2 teaspoon of the olive oil. Fold the foil over the cloves to completely seal and form a packet. Place on the baking sheet next to the broccoli.

Step 4

Roast, flipping the broccoli and packet halfway through, until the broccoli is charred in spots on both sides, about 15 minutes total. Meanwhile, dice 1 medium yellow onion. Chop 1/2 medium head of cauliflower into 1-inch florets and dice the stem into 1/2-inch pieces. Peel 2 medium Yukon gold potatoes and cut into 1-inch cubes.

Step 5

When the broccoli is ready, set aside and leave the garlic to cool in the packet.

Step 6

Heat the remaining 1 tablespoon olive oil in a large saucepan or Dutch oven over medium heat until shimmering. Add the onion and sauté until mostly translucent, 3 to 4 minutes. Add the cauliflower florets and stems, potatoes, 4 cups low-sodium vegetable broth, the remaining 1 teaspoon kosher salt, and 1/2 teaspoon black pepper. Increase the heat to high and bring to a boil.

Step 7

Reduce the heat to low, cover, and simmer until the vegetables are almost tender but are not quite cooked through, about 10 minutes. Meanwhile, unwrap the roasted garlic and peel the cloves. Pick the leaves from 1/2 bunch fresh parsley until you have 1/2 cup and coarsely chop. Juice 1/2 medium lemon until you have 1 tablespoon juice.

Step 8

Add the roasted broccoli, garlic, and 2 tablespoons nutritional yeast to the soup and stir to combine. Cover and simmer until all the vegetables are fork-tender, 5 to 10 minutes.

Step 9

Add the parsley and lemon juice and turn off the heat. Working in batches, transfer the soup to a blender and blend until smooth and creamy. (Alternatively, blend right in the pot with an immersion blender.) If the soup is too thick, blend in up to 1 more cup water or vegetable broth to reach the desired consistency. Taste and season with more kosher salt as needed.

Step 10

Serve immediately topped with a small drizzle of olive oil and a handful of croutons, if desired. If the soup isn’t quite hot enough, reheat in the pot on the stove over medium-low heat, stirring often.