Preparation Fill large bowl with cold water. Working with 1 Yukon Gold potato at a time, peel, then cut into 1/8-inch-thick rounds and place in bowl with water. Repeat with sweet potatoes. Combine cream, butter, and garlic in medium saucepan; bring to simmer. Remove from heat. Mix all herbs in small bowl. Mix sea salt and black pepper in another small bowl. Butter 13x9x2-inch glass baking dish. Drain potatoes, then pat dry with kitchen towels. Transfer half of potatoes to prepared baking dish. Use hands to distribute and spread evenly. Sprinkle with half of salt-pepper mixture, then half of herb mixture. Sprinkle with half of cheese. Repeat with remaining potatoes, salt-pepper mixture, herb mixture, and cheese. Pour cream mixture over gratin, pressing lightly to submerge potato mixture as much as possible. DO AHEAD: Can be made 6 hours ahead. Cover with plastic wrap and chill. Remove plastic wrap before baking. Preheat oven to 400°F. Cover gratin tightly with foil. Bake 30 minutes. Uncover; bake until top of gratin is golden and most of liquid is absorbed, about 25 minutes longer. Let stand 10 minutes; serve.