Heat the oven to 425F. Cut the broccoli into small, even florets and trim the tough end off the stem, then dice the tender stem finely. Set aside about 4 cups of the nicest florets for roasting and keep the rest, plus the diced stem, for the pot.

Toss the 4 cups of florets with the tablespoon of olive oil and the quarter teaspoon of fine salt on a sheet pan. Spread them in a single layer and roast for 18 to 20 minutes, turning once, until the tips are browned and crisp at the edges.

While the broccoli roasts, heat the 2 tablespoons of olive oil in a large pot over medium heat. Add the onion, carrots, and celery and cook for 6 to 7 minutes, stirring now and then, until the onion turns translucent and the edges start to soften.

Stir in the garlic and cook for 1 minute, until it smells sweet rather than sharp. Add the potato, the diced broccoli stem, the remaining florets, 4 cups of vegetable broth, and the black pepper.

Bring the pot to a boil over high heat, then lower the heat and simmer for 12 to 15 minutes, until the potato cubes crush easily against the side of the pot and the stems are tender.

Drain the soaked cashews and add them to a blender with the three quarters cup of vegetable broth, nutritional yeast, Dijon mustard, apple cider vinegar, smoked paprika, garlic powder, turmeric, and the half teaspoon of salt. Blend on high for a full minute or two, until the sauce is completely smooth and no grit remains.

Let the soup base cool for a few minutes, then blend it in batches until smooth, filling the blender no more than halfway each time. Return the blended soup to the pot and stir in the cashew sauce.

Warm the soup over low heat, stirring, then taste for salt and acidity. Fold in the roasted broccoli off the heat, ladle into bowls, and serve.