Put the broccoli, cauliflower, shallot, or onions, and stock into a large saucepan. Bring to the boil, cover, then reduce the heat and simmer for 10 minutes, or until the florets are tender. Purée in a food processor or with a hand-held mixer.
Return the soup to the pan and add the milk and pasta. Gently bring it to a steady simmer, then cover and cook for a further 10 minutes, or until the pasta is tender.
Stir in the cheese and chives, reserving some chives for a garnish, and simmer for a few more minutes, stirring occasionally, until the cheese has melted and the soup has thickened slightly. Do not boil it or the cheese will become stringy.
Season to taste, garnish with the reserved chives and a sprinkling of nutmeg, and serve.
Variation: use all broccoli or all cauliflower, if you prefer.