Preheat oven to 425F. Grease a 15 x 10-inch baking pan with oil.
Combine potatoes, cream, thyme, salt, pepper and nutmeg in a large bowl. With a slotted spoon, transfer potatoes to a pan, spreading them in a single layer. Reserve cream mixture. Bake about 30 minutes, until largest potato is easily pierced with a fork.
Remove from oven. With a spatula, slide potatoes together. Drizzle with remaining cream mixture. Sprinkle with cheese. Return pan to oven on top rack until cheese is melted and begins to brown. Transfer to a platter and serve immediately.