In a medium saucepan melt butter then cook leeks over medium heat until softened, about 3 minute Increase heat to medium-high, add cream, broth and thyme, stir and bring to a boil. Reduce heat to medium and simmer until liquid reduces to about 1 1/3 cups, about 5 minute Stir in salt, pepper and nutmeg.
Using a sharp knife or mandolin, thinly slice potatoes into rounds. In a 2-qt baking dish, starting with white potatoes as the base, alternately layer potatoes, switching directions for each layer. Pour sauce evenly over the potatoes and bake, covered with aluminum foil, 1 hour 30 minute Uncover, sprinkle with cheese and bake until cheese is melted and bubbly, about 20 minute.