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Trim 1/2 inch off broccoli stalks; remove the tough outer layer with a vegetable peeler. Cut the broccoli lengthwise so the florets attached to the long stalks are 1 to 2 inches wide. Bring 1 inch of water to a boil in a Dutch oven fitted with a steamer basket. Steam the broccoli until tender, 5 to 7 minutes.
Meanwhile, whisk flour and 1/4 cup milk in a small bowl until smooth. Heat the remaining 3/4 cup milk in a saucepan over medium-low heat until steaming. Whisk in the flour mixture; cook, whisking, until thickened, 2 to 4 minutes. Remove from the heat; add cheese, salt, pepper and nutmeg (if using). Drizzle over the broccoli. Serve warm.