Heat a tablespoon of oil in a soup or large pot over low-medium heat and add the onions, celery, carrot and potato. Season with salt and pepper and sauté for 7 minutes or until soft.
Meanwhile, prepare the broccoli. Trim the woody bases from each stalk (cut about 1cm off) and separate the stalk from the tops of the broccoli. Slice the remaining stalk in half lengthways and then slice them. Chop the florets into small-ish pieces (around 1-inch) but keep them separate. We are going to cook the stalks first and add the florets later. You don't need to get too fussy chopping the florets, just try and get them into similar size pieces for even cooking.
Stir the garlic into the pot and cook for another 30 seconds (or until fragrant) before adding the nutritional yeast. Give it a good stir and then add the broccoli stalks and cashews.
Add the stock and increase the heat to bring the soup to a gentle boil. Turn the heat down and simmer for around 20 minutes.
Add the chopped broccoli florets and the extra water and cook for another 4 -5 minutes or until tender.
Remove the pot from the heat.
You can blend your soup in a stand blender or use an immersion (stick) blender in the pot. For the stand blender, carefully add a few cups of the stock and vegetables to your blender (never fill your blender past the maximum fill line! You'll end up with hot soup everywhere) Blend until smooth, then transfer to a heat-proof jug or bowl (a jug is easier if you have one) while you blend the rest of the soup in similar batches. You can use an immersion blender in your soup pot to blend your soup, it just may not be as creamy. Transfer the soup back to the pot and over a low heat and add the mustard and cheese. Gently stir the soup until the cheese is melted. Add more if you like, it's up to your personal taste.
Serve with a sprinkling of dill and crunchy croutons.