To prepare béchamel sauce: Melt the butter in small pot over medium heat. Remove pot from heat and whisk in flour. Return pot to medium heat, gradually whisk in all the milk and cream, making sure the sauce is smooth between each addition. Season with salt.
Lower heat, cover pot and simmer gently, stirring occasionally, for about 20 minutes. The sauce should be thick enough to coat the back of a spoon and not run off. Season with more salt if necessary, then add pepper and nutmeg, if using. If the sauce is too thick, add a little more milk. If it is too runny, simmer for a bit longer.
To finish the dish: Add the potatoes to the sauce. Stir carefully from time to time, while heating the mixture over a low heat. Make sure the sauce doesn't burn, but also take care not to break up the potatoes too much.
Once the potatoes are hot enough, and just before serving, add the dill and season well with salt and quite a bit of white pepper.
Tester's notes: We used red new potatoes, with the skins, and cut them into a 1/2-inch dice. This dish is reminiscent of a warm potato salad.
Nutrition information per each 6 servings: