Warm a large pot over medium heat and add the olive oil or vegan butter.
Sauté the onion, carrots, and celery with a pinch of salt for 5–7 minutes, until softened and fragrant.
Stir in the garlic and cook for 30 seconds. Add the potato and chopped broccoli stems (save most of the florets for later), then pour in the vegetable broth. Bring to a simmer.
Cover and cook for 10–12 minutes, until the potatoes and stems are tender.
This forms the base that will blend into a creamy soup.
While that cooks, soak the cashews in hot water if you haven’t already. Drain before blending.
Transfer about two-thirds of the pot (broth and veggies) to a blender. Add the soaked cashews, oat milk, nutritional yeast, miso, Dijon, onion powder, paprika, and turmeric.
Blend until completely smooth and velvety.
Pour the blended mixture back into the pot. Stir in the reserved broccoli florets. Simmer for 5–8 minutes, until the florets are tender but still bright green.
Finish with lemon juice, then taste and adjust.
Add more salt, pepper, or nutritional yeast for a cheesier flavor. If you want more heat, sprinkle in red pepper flakes.
For a thinner soup, add a splash of broth or milk. For a thicker soup, simmer a few extra minutes to reduce slightly.
Serve hot with crusty bread, vegan croutons, or a sprinkle of chives.