Fill large bowl with cold water. Working with 1 potato at a time, peel, then cut into 1/8-inch-thick rounds and place in bowl with water.
Combine cream, butter, and garlic in medium saucepan; bring to simmer. Remove from heat.
Mix all herbs, salt, and pepper in small bowl.
Butter 13×9×2-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 herb mixture, then half of cheese. Repeat with remaining supplies. Pour cream mixture over gratin, pressing lightly to submerge potato mixture as much as possible. (All of this can be done up to 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, and bake until top of gratin is golden and most of liquid is absorbed, about 25 minutes longer. Let stand 10 minutes; serve.