Set the oven at 350 and add the sweet potato whole with the skin on. Allow it to roast until soft to the touch for about 25-40 minutes depending on its size.
In a soup pot over medium heat place half of the butter and the chopped onion. Sauté until wilted for about 5 minutes.
Meanwhile, chop the broccoli, mincing up the stalks. Reserve about 1 cup of the florets, chopped small to use as garnish.
Add the remaining broccoli and potato chunks. Sauté for a few minutes and then pour in half of the broth and garlic. Bring up to a boil and reduce to a simmer. Cook for about 5-8 minutes until the broccoli and potatoes are tender. Stir in the spinach or greens.
Peel the sweet potato once soft.
In batches, transfer the soup and sweet potatoes to a blender and puree until silky smooth. Adding more broth as needed to thin the soup. Blend in the shredded cheese. Pour all of it back into the soup pot over low heat. Season with salt and pepper to taste.
Meanwhile, saute the tiny broccoli florets in the remaining butter. Add a generous splash of water, simmering until the broccoli feels tender. Season with a pinch of salt and pepper.
Serve the hot bowls of soup with a sprinkle of the tiny cooked broccoli and a few shreds of cheddar.
