Heat oil in a large soup pot over medium heat. Add the onion, carrots, celery, and garlic and cook until soft, about 3-5 minutes.
Add the flour and stir until smooth. Add in the poblano and continue to cook to get rid of the flour taste.
Add the broth, almond milk, and potatoes. Bring to a boil, then reduce heat, and simmer until potatoes are almost soft, about 8-10 minutes.
Add the broccoli and return to a simmer. Cook uncovered until the broccoli is tender, about 5 minutes.
Stir in the nutritional yeast and smoked paprika. Adjust salt and pepper to taste.
Remove 1-2 cups of soup, scooping up as little broccoli as possible. Puree in a blender or use an immersion blender. Add back the soup that was removed and stir. Alternatively you can blend the entire soup for a creamier consistency.
Top with fresh cilantro or parsley.