Preheat the Oven: Set your oven to 325°F (163°C).

Infuse the Cream: In a small saucepan, combine the heavy cream, kosher salt, and minced garlic. Simmer over low heat for 5 minutes to allow the garlic to infuse the cream. Remove from heat and set aside.

Prepare Potatoes: Using a mandoline slicer, thinly slice the potatoes to a thickness of 1/8 inch.

Sauté Shallots: In a 12-inch cast iron pan, melt the butter over low heat. Add the diced shallots and sauté until caramelized, about 5 minutes.

Layer the Potatoes: Arrange the sliced potatoes in a spiral pattern over the caramelized shallots in the cast iron pan.

Add Cream: Pour the infused cream mixture evenly over the potatoes.

Bake: Cover the pan tightly with aluminum foil and bake in the preheated oven for 1 hour and 15 minutes.

Broil the Cheese: Remove the pan from the oven and increase the oven temperature to broil. Uncover the potatoes and top with grated Gruyere and Parmesan cheeses. Sprinkle with fresh thyme.

Finish Under Broiler: Return the pan to the oven and broil for 5 minutes, or until the cheese is crispy and bubbling.

Serve and Store: Remove from the oven and serve warm. Leftovers can be stored in the refrigerator and reheated the next day.