Heat the oil in a large saucepan over medium heat. Add the onions and 1/2 teaspoon salt and cook until light brown, about 7 minutes. Add the celery, garlic and 1/4 teaspoon pepper and cook for 5 minutes. Add the potatoes, 4 cups water and 1/2 teaspoon salt, raise the heat to high and bring to a boil. Return the heat to medium, cover and cook until the potatoes are tender, about 15 minutes. Add the broccoli, cover and cook until the broccoli is bright green, about 5 minutes.
Transfer the soup to a blender; add the soy milk and puree until smooth, leaving the filler cap slightly open to let steam escape (or puree the soup in the pot with an immersion blender). Return the soup to the saucepan and bring to a simmer; stir in the nutritional yeast and nutmeg. Add water if needed to adjust consistency and add salt and pepper to taste.
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