Heat the oil in a large soup pot over a medium heat. Once shimmering, add the leek and spring onion greens and stir to coat. Cook for 2-3 minutes until fragrant.
Add the chopped potatoes, chopped broccoli stems (not the florets, yet) nutritional yeast (if using) and stock or water. I recommend adding the lesser 1000ml (1 litre) of stock/water first, then adding more if need be.
Stir, then top with a lid and cook for 10-20 minutes or until the potatoes are completely cooked through.
Once everything is totally cooked, turn off the heat and use your soup stick (immersion blender) or blender to process the soup. If you’re using a blender without a steam valve, you will need to let the soup cool completely or you risk exploding the blender.
Blend until you achieve your desired consistency, turn the heat back onto a low-medium. Add the finely chopped broccoli florets and cook the soup for an additional 10 or so minutes or until the florets are cooked to your desired consistency. Larger chunks will take longer to cook.
Remove the soup from the heat and stir in the milk. Add the grated cheese gradually to ensure it doesn’t overcook and become stringy. Season with plenty of salt, pepper and lemon juice according to your tastes.
You can serve as is, with some cream or croutons, or with some chilli oil/chilli crisp for spice.
Leftovers keep well in the fridge for a number of days and can be frozen.