Lots of the recipes I found for vegan broccoli cheddar soup used milk alternatives, nuts, flour, cornstarch, and/or vegan cheese. I was looking for something simpler.

2 Tbsp olive oil
1/2 medium onion, medium dice
2 stalks celery, medium dice
1 medium sweet potato, small dice
2 cloves garlic, thin slice
Kosher salt and freshly ground black pepper
1 1/2 cups arugula
1 small head broccoli, cut into small florets
1/2 cup nutritional yeast

1. Heat the oil in a pot over medium-high heat.
2. Add the onion, celery, sweet potato, and garlic to the pot. Season with salt and pepper.
3. Saute, stirring occasionally, until tender, about 10 minutes.
4. Pour water into the pot and cover the vegetables by 3 inches. Bring to a boil, then reduce to a simmer and cook for 20 minutes.
5. Stir in arugula and cook for another minute. Puree with an immersion blender.
6. Add broccoli florets and nutritional yeast and simmer for another 15-20 minutes, or until the broccoli is soft.
7. Adjust seasoning to taste and serve.

Notes: yum. Love the color the sweet potato lends to the soup, which mimics traditional broccoli cheddar soup. The nutritional yeast is a powerhouse, giving the finished product a rich, cheesy, almost fermented flavor. The arugula simply boosts the nutrition profile, but is not essential; it can be omitted, or substituted with nearly any other type of green leafy vegetable.