Broccoli: peel the tougher and fibrous outer layers of the stalks. Chop off the broccoli heads from the stalks.
For the stalks, I sliced the stalks horizontally in half before slicing into small half-circle pieces. Set aside.
For the broccoli heads, simply separate these into florets. Roughly chop the florets into smaller chunks. Set aside.
Potatoes: Peel the potatoes and then chop into 1 to 2-inch (2.5 to 5 cm) chunks.
Heat a large dutch oven or pot over medium high. Once hot, melt the vegan butter. Add the onion and garlic. Sauté until the onion is translucent, around 2 minutes.
Add in the diced potatoes and broccoli stalks into the pot. If you want extra flavour, you can opt to slightly brown and char the broccoli.
Pour in the vegetable broth. Add in the miso paste, if using. Season with salt and pepper to taste. Cover the pot and leave to boil.
Leave the potatoes and broccoli stalks to cook for 8-10 minutes until fork tender.
Once tender. Allow to cook for a few minutes before transferring to a blender. Blend until smooth and creamy. You can also use an immersion blender.
Place back the soup into the pot. Add in the oat milk, more salt to taste (if needed), nutritional yeast (if using), and vegan cheddar shreds.
Mix in the chopped broccoli florets. Leave the broccoli florets to cook for 4-5 minutes or until tender to your liking.
Serve the soup while hot and then top with more shredded cheddar cheese. Enjoy with bread of your choice.