When the potatoes are finished cooking, immediately drain and mash them while hot. Have your cream and butter heated and ready to add in right then. A few lumps are OK. If you overstir or let the potatoes cool before mashing, they'll be gluey.
Place cut potatoes in a 6-quart saucepan and cover with cold water. Add 1 teaspoon sea salt, cover and bring to a simmer. Cook for 20 minutes.
Meanwhile, in a small saucepan over low heat, melt butter with cream, 1 tablespoon sea salt, and a pinch of white pepper.
When potatoes are cooked thoroughly (remove a piece and taste to ensure tenderness), drain in a colander. While still hot, pass potatoes through a food mill with a medium sieve attachment, or through a potato ricer, and put back into the pot in which they were cooked.
Slowly pour the warm butter-cream mixture into the potatoes; incorporate gently with a wooden spoon. Taste and adjust seasoning. Garnish with fresh chives or basil. Serve immediately.