Bring the water to a boil; add the salt. Add the potatoes, reduce the heat to medium, and cook until the potatoes are tender, about 35 min. Drain immediately.
If you want to peel the potatoes, do this as soon as they're cool enough to handle. (Most of the peel will be removed by the food mill.)
While the potatoes are cooking, heat the olive oil in a small sauté pan over low heat. Add the onion and sauté until translucent and soft, about 10 min.
Add the sautéed onion to the drained potatoes and grind the vegetables through a food mill using a fine mesh. Slowly add the hot milk to the potatoes, stirring constantly.
Grind the potatoes through the food mill again, this time using the finest mesh.
Add the herbs to the potatoes and season to taste with salt, pepper, and nutmeg. Keep warm in a double boiler, uncovered, until served.