Light the broiler and place the oven rack six inches from the heat source. Cut and set aside some of the broccoli florets to get 6 small pieces, about an inch in all-around bulk.

In a large pot over medium heat, warm 4 tablespoons of the olive oil and add the onion, celery, fennel, carrot, remaining broccoli florets and stems and star anise. Toss to coat in the oil. Cover and steam in the olive oil for 5 minutes. Stir in the garlic and ginger and steam, covered, for another 3 minutes. Add the potato to the pot and toss gently.

Add the vegetable broth and 1 cup of water. Season to taste with salt and bring to a simmer, covered. Continue to simmer the soup until all the vegetables are fork tender,about 35 to 40 minutes.

While the soup is simmering, toss the broccoli florets with the remaining olive oil and some salt, and place on a baking sheet. Broil for 5 to 7 minutes, turning, until lightly charred. Remove and set aside.

In a small food processor, pulverize the cashews, vinegar, mustard, dill and lemon juice to a thick paste.

Remove the star anise from the soup pot and discard. Using an immersion blender, puree the soup until chunky. Add the cashew paste and continue puréeing until the consistency is thick and creamy. Adjust the seasoning with additional salt, vinegar or lemon juice. Serve hot in individual bowls garnished with charred florets and a little olive oil.