Preparation steps

• Fill a large bowl with cool water. Take 1 Yukon Gold potato at a time, peel, then cut into 1/8-inch-thick rounds and place in 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. 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. (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.