Creamy Potato and Leek Gratin

9 medium leeks ( about 3 lb; white and pale green parts only)
3 Tbsp unsalted butter
2 lb russet (baking) potatoes
1 1/2 cups heavy cream
1 cup whole milk
2 tsp thyme leaves

Preheat oven to 400°F with rack in middle. Generously butter a 3-qt shallow baking dish.
Cut a round of parchment paper to fit just inside a 12-inch heavy skillet, then set parchment aside.
Halve leeks lengthwise, then cut crosswise into 1 1/2-inch pieces and wash.
Cook leeks in butter with 1/2 tsp salt and 1/4 tsp pepper, covered with parchment round, in skillet over medium heat, stirring occasionally, until tender, 10 to 12 minutes.
Meanwhile, peel potatoes and slice crosswise 1/16 inch thick with slicer.
Transfer to a large heavy pot with cream, milk, thyme, 1 tsp salt, and 1/2 tsp pepper and bring to a boil over medium heat, stirring occasionally (liquid will thicken).
Stir in leeks, then transfer to baking dish.
Bake, uncovered, until potatoes are tender, 45 minutes to 1 hour.
Let stand 10 minutes before serving.
Do Ahead
Gratin can be baked 2 days ahead and chilled. Let stand at room temperature 30 minutes, then reheat, covered, in a 350°F oven until hot, about 30 minutes.