Cut the boiled potatoes into cubes.
Warm the milk in a saucepan, set aside.
In a heavy saucepan, melt the butter over medium to high heat. Add the flour, and stir for about 2-3 minutes, letting the flour cook without it turning a dark colour or burning. Slowly add the warmed milk and whisk constantly. Lower the heat and bring to a slow simmer. Add nutmeg and salt and pepper to taste. Continue whisking until the sauce has thickened, about 5 minutes.
Add the potato cubes into the sauce, until just warmed. Add the chopped dill.
Place in a serving dish and serve immediately with for example marinated salmon (gravlax).