In a soup pot, heat 2–3 tablespoons of vegetable broth over medium-high heat. Sauté the onion and garlic until fragrant, about 3 minutes. Add the celery and cook for 3 minutes more.
Add the remaining vegetable broth, cannellini beans, broccoli florets, and baby spinach. Bring to a boil, then reduce the heat to low and simmer until the broccoli is tender, about 8 minutes.
Remove from the heat. Add the parsley, thyme, nutritional yeast, black pepper, and coconut milk. Use an immersion blender to blend until smooth. Alternatively, carefully transfer the soup to a blender, blend until smooth, and return it to the pot.
Taste and adjust seasonings as desired. Reheat if necessary.
Ladle into bowls and garnish with sesame seeds and a few extra broccoli florets, if desired. Serve and enjoy!