Pour oil into a large heavy bottom pan. Heat over medium heat. Add the onions and cook, stirring occasionally, until translucent - about 10 minutes. Add the garlic, again stirring occasionally, cook for 1 -2 minutes. Add the spices and cook 1 minute more. If the onions or garlic begin to stick at any time add a small amount of broth.
Once the onions are cooked through, add the broth, potatoes and cauliflower to the pot. Bring to a simmer. Cover and cook for 15 minutes until potatoes are able to be pierced by a fork.
Remove half of the cooked vegetables and place in a large bowl.
Add the broccoli and carrots to the broth and cover. Continue to cook for 10 minutes more.
While the broccoli is cooking, use an immersion blender to puree the potatoes and cauliflower. Add the coconut milk and blend a little more until it is well mixed and smooth.
Uncover the pot. Add the potato mixture to the soup and stir together. If you want it to thicken, cook without the lid for up to 5 minutes more. Remove from heat and stir in the nutritional yeast until dissolved. Serve immediately.