Fill a saucepan with 1" water and add steamer basket. Bring to a boil and add the carrots and potato to the steamer basket. Cover and cook until fork tender, about 10-15 minutes. Transfer to a food processor or blender and allow to cool off for a few minutes.
Meanwhile, add the olive oil and onion to a large pot. Saute for 3-5 minutes or until onion is translucent and tender. Stir in the broccoli, 2 cups of the broth, and coconut milk. Bring to a simmer.
Add the reserved 1 cup of vegetable broth, yeast, paprika, and soy sauce to the food processor/blender with the steamed carrots and potato. Puree until smooth and then stir into the pot with the broccoli. Cook for 7-10 minutes or until mixture is starting to simmer.
Stir in the red wine vinegar and season with salt and pepper.
Pour about 1/2 of the soup into the same food processor/blender and blend until smooth OR use an immersion blender to puree some of the soup. (I still like to leave some broccoli pieces whole). Transfer back into the pot with the rest of the soup. Stir in vegan cheddar cheese if using.
To serve, divide into bowls and top with croutons, paprika, vegan cheese, coconut bacon, or whatever other toppings you have on hand.