Peel and quarter turnips. In a large saucepan of boiling salted water cook turnips until tender, 15 to 20 minutes, and drain in a colander.
In a heavy saucepan bring milk and cream just to a simmer and keep hot over low heat.
Chop shallots. In a 4-quart heavy kettle cook shallots in butter over moderately low heat, stirring, until softened.
Add thyme, salt, peppercorns, cloves, and bay leaves and cook, stirring, 1 minute. Add flour and cook roux, stirring, 3 minutes.
Whisk in hot milk mixture all at once and bring to a boil over moderately high heat, whisking occasionally, 15 minutes.
Pour sauce through a sieve into a large heavy saucepan and discard solids.
Into sauce stir white pepper, nutmeg, and salt to taste. Turnips and sauce may be made up to this point 1 day ahead and kept separately in bowls, covered and chilled.
Return sauce to a simmer and add turnips. Cook mixture, covered, over moderately low heat, stirring occasionally, until turnips are heated through.
Garnish turnips with parsley.