9 medium leeks (about 3 lb; white and pale green parts only)
3 Tbsp unsalted butter
2 lb russet (baking) potatoes
1½ 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 1½-inch pieces (you should have about 8 cups). Wash leeks.
Cook leeks in butter with ½ tsp salt and ¼ 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 ½ 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.
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.