Bring steaming water to a simmer below a steamer basket in a covered pot, keeping the basket above the water. Add potatoes and steam for 20 to 25 minutes until very tender, adding some of the measured hot water if needed to keep the pot from drying.
Meanwhile, melt butter in a soup pot over medium-low heat and cook shallots for 4 to 5 minutes until soft without browning. Add broth and bring to a gentle simmer.
Warm milk in a small saucepan until steaming. Pass the hot drained potatoes through a potato ricer directly into the broth, then stir gently with a whisk to distribute them without beating.
Stir in warm milk and mascarpone until smooth, then add ham, white pepper and nutmeg. Warm over low heat for 5 to 7 minutes until ham reaches 165°F, avoiding a hard boil.
Remove from heat and stir in chives. Taste before adding up to the measured salt.
Divide among six bowls and serve while the soup is smooth and steaming.