In a 5-quart kettle, combine artichokes, potatoes, salt, and milk with enough water to cover vegetables by 2 inches; simmer until vegetables are tender, about 25 minutes.
Drain vegetables in a colander and return to kettle.
With a potato masher, mash vegetables with butter and salt and pepper to taste until smooth. Serve. Vegetables may be made 3 days ahead and chilled, covered. Bring vegetables to room temperature before reheating, covered.