In a blender, whirl milk, chilies, and 1/2 teaspoon salt until smooth. Stir in cream. Reserve 1/3 cup of the cream mixture.
Peel and rinse sweet potatoes; cut crosswise into 1/4-inch-thick slices. In a shallow 2 1/2- to 3-quart casserole, arrange about a third of the sweet potatoes in an even layer, overlapping slices; evenly drizzle with about a third of the remaining cream mixture. Repeat to make two more layers of the sweet potatoes and cream.
Bake (covered, if using drier, pale-fleshed sweet potatoes; see notes) in a 400° regular or convection oven for 40 minutes. Uncover, if covered, and drizzle top evenly with about 3 tablespoons of the reserved cream mixture. Continue baking, basting occasionally with reserved cream mixture or pan juices, until potatoes are tender when pierced and top of gratin is browned, 15 to 25 minutes longer. Let stand about 5 minutes before serving. Scoop out portions with a large spoon.