2Fill a large bowl with cold water. Peel and slice each potato 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 kosher salt and black pepper in another small bowl.
Drain potatoes and pat dry with kitchen towels. Transfer half of potatoes to prepared baking dish, spreading out evenly. Sprinkle with half of salt pepper mixture, then half of herb mixture.
Sprinkle with half of the 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.
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 before serving.