|Cut the broccoli tops into large florets. Trim and peel the stalks, removing any fibrous or woody parts. Cut the stalks into 1" chunks.
Place the broccoli, stock, onion, oatmeal, and salt into the pot. If using dried dill, add at this time.
Cover the pot, bring to a boil, reduce heat and simmer until the broccoli is very soft and the oatmeal is cooked, about 15-20 minutes.
Puree the soup in a blender, food processor or with a hand blender.
Return to the soup pot and stir in fresh dill and salt to taste.
Simmer just long enough to reheat the soup.