Prepare the broccoli: separate florets from stalks. Using a peeler or a knife, peel off skin of the stalks to remove the hard outer layer. In separate piles, chop up the stalks and the florets into small pieces, about 1 inch thick.
In a 8 quart or larger pot on medium heat, add olive oil and onions to sautee. After three minutes, add the garlic. Sautee until translucent about 8 minutes.
Add potatoes and chopped broccoli stalks. Note: if you want a chunkier soup, add ¾ of the chopped stalks now and save ¼ to be added at the end.
Cover the vegetables with stock and set to boil. Once boiling, turn the heat down to low. Add the cinnamon, nutmeg, salt, and pepper. Stir and cover. Cook for 20-25 minutes. Add the florets and cook, covered, for another 5 minutes.
Using an immersion blender, blend the soup together. (You can also use a food processor or stand blender if you don't have).
If you want the chunkier soup, add the remaining chopped stalks to the soup and cook for an additional 5-10 minutes.