Take the broccoli apart, separating the florets from the stems. Peel the stiff outer layers of the broccoli stalks after trimming and discarding the bottoms. The stems should be chopped finely, while the florets should be chopped roughly.
Heat a sizable pot over medium heat while spraying it with nonstick cooking spray. Stirring often, simmer the potatoes, onions, and broccoli stems for 7 to 10 minutes, or until they are tender. For about two minutes, while stirring, heat the flour until just barely browned. Bring to a boil while stirring in the broth. Cook, periodically stirring, for 12 to 15 minutes, or until the sauce has thickened and the veggies are cooked. Reduce the heat to maintain a simmer.
In the meantime, put 1/2 cup of water and the saved florets in a small pot. Bring to a boil, cover, and steam for about 5 minutes, or until the florets are bright green and crisp-tender. Add the nutmeg and the entire contents of the pot with the florets to the soup. After combining everything, turn off the heat. Add the milk, Worcestershire, and Cheddar by stirring. Add salt and pepper to taste. Add the scallions as a garnish.
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