Preheat Oven: Preheat the oven to 325°F (165°C).
Prepare Potatoes: Wash and thoroughly dry the potatoes, leaving the skins intact. Slice them into uniform ⅛-inch rounds using a sharp knife or mandolin. Set aside.
Infuse Cream Mixture: In a small saucepan over low heat, combine the heavy cream, salt, and minced garlic. Simmer gently for 5 minutes, stirring occasionally. Remove from heat and set aside.
Caramelize Shallots: Melt the butter in a 12-inch cast iron skillet over low heat. Add the diced shallots and cook, stirring frequently, until softened and lightly caramelized (5–7 minutes). Remove from heat.
Layer Potatoes: Arrange the potato slices in a tight, overlapping spiral pattern over the caramelized shallots, beginning at the outer edge of the skillet and working inward.
Assemble and Bake: Pour the infused cream mixture evenly over the potatoes. Cover the skillet tightly with aluminum foil and bake on the center rack for 1 hour and 15 minutes.
Broil Cheese Topping: Remove the skillet from the oven and discard the foil. Increase the oven temperature to broil (500°F/260°C). Sprinkle the grated Gruyère and Parmesan cheeses evenly over the potatoes, followed by the fresh thyme or chives. Broil for 3–5 minutes, or until the cheese is golden and bubbling.
Rest and Serve: Allow the gratin to cool for 15 minutes to set before serving.