Place the potatoes in a 2-quart saucepan with 1 teaspoon of the salt and cold water to cover. Bring to a boil, lower the heat and simmer, covered, until completely tender, about 20-30 minutes. Test the potatoes by piercing them with a paring knife; there should be no resistance. Drain well in a colander, then put back in pot and keep warm.
Combine the butter, heavy cream and milk in another saucepan and heat gently just until the butter has melted. Keep warm.
Mash potatoes, slowly stirring in half of the milk and butter mixture. Mash in 3/4 of the grated cheddar cheese and blend in as much of the remaining milk mixture as needed while hand-mashing. Season to taste with salt and white pepper. Just before serving, top with remaining cheddar and chives; serve hot.