Begin by preheating your oven to 350°F and positioning the oven rack in the center. Generously butter an 8-inch (or 2-quart) baking dish to prevent sticking.
In a large bowl, combine the thinly sliced potatoes with salt and pepper, ensuring they are evenly coated with the seasoning.
Start layering the potatoes in the prepared baking dish, arranging them so that the edges slightly overlap in a single layer. Sprinkle a quarter of the grated Parmigiano-Reggiano over the potatoes, followed by pouring a quarter of the heavy cream evenly over the cheese. Repeat this process to create a total of four layers of potatoes, cheese, and cream. Pour any remaining cream over the final layer.
Transfer the dish to the oven and bake, uncovered, for 60 to 75 minutes. The dish is ready when the potatoes are tender when pierced with a knife and the top is beautifully golden brown. Once baked, allow the dish to rest on the counter for about ten minutes before serving. If desired, garnish with fresh thyme before serving.
Make Ahead: If needed, you can assemble the dish a day in advance. Cover tightly with plastic wrap, pressing the wrap directly against the potatoes to minimize discoloration. Refrigerate until ready to bake. Be aware that the top layer of potatoes may darken slightly in the fridge, but this will be less noticeable after baking.