Cut away the thick stem at the base of the cauliflower and tear off the green leaves. Separate the flowerets and wash them under cold running water. Reserve 10 small flowerets, and chop the rest coarsely. Combine the stock and water in a 2 to 3 quart saucepan, and bring to a boil over high heat. Drop in the whole flowerets, and boil briskly, uncovered, for 10 minutes, or until they are tender but still somewhat resistant to the point of a small, sharp knife. Remove the flowerets and set them aside in a bowl. Reserve the stock.
Melt the butter over moderate heat in a 4 quart stainless-steel or enamel saucepan. Stir in the flour and cook over low heat, stirring constantly, for 1 or 2 minutes. Do not let flour brown. Pour in the stock and the milk, beating constantly with a whisk. Cook, stirring, until the mixture comes to a boil and is smooth and somewhat thick. Reduce heat to low, and simmer for 2 or 3 minutes.
Then add the chopped cauliflower, salt, pepper and nutmeg. Simmer, half covered, for 15 minutes, or until the cauliflower is soft enough to be easily mashed against the side of the pan. Pour the cauliflower and all of its cooking liquid into a sieve set over a bowl. With a wooden spoon, force the cauliflower through the sieve.
Return the puree to the pan. Beat the egg yolk with a fork or whisk to break it up, then beat 1/2 cup of hot puree, 2 Tblsp. at a time. Now whisk the mixture back into the saucepan. Add the reserved flowerets and cook over moderate heat for 2 or 3 minutes, stirring occasionally. Do not let it boil. Add the lemon juice, taste for seasoning, and serve.