Preheat the oven to 375 degrees F. Coat a 13- x 9-inch baking dish with nonstick cooking spray. Peel the potatoes and set aside.
Add the heavy cream, whole milk, 3 or 4 thyme sprigs, and ½ teaspoon salt to a small saucepan and place over LOW heat. Cook, stirring frequently, until the edges just begin to bubble, about 5 minutes (don’t allow to boil). Remove from the heat and set aside.
Thinly slice the peeled potatoes (⅛- to ¼-inch thick or mandolin setting between 1.25 to 1.33 mm).
Cover the bottom of the prepared baking dish with ⅓ of the potatoes, spreading them out evenly over the bottom. Sprinkle evenly with ½ teaspoon salt, thyme leaves from 1 or 2 sprigs, a light sprinkling of pepper, and ½ of the Parmesan. Repeat layering once more with another ⅓ of potatoes, ½ teaspoon salt, more thyme leaves, pepper, and the remaining Parmesan. End with a final layer of potatoes (don't add any seasonings on the top layer).
Remove the thyme sprigs from the warm cream mixture and pull your fingers along the sprigs to remove some of the leaves, dropping them into the cream mixture. Discard the sprigs. Pour the cream mixture evenly over the top of the potatoes. Sprinkle evenly with the remaining salt and additional thyme leaves, to taste (omit pepper and Parmesan on top layer).
Cover the baking dish tightly with foil. Bake for 20 minutes. Remove the foil and continue to cook for an additional 35 to 45 minutes, until the potatoes are very tender and browned. Cooking time will vary depending on the thickness of your potato slices. Remove the pan from the oven and allow the potatoes to rest for 10 minutes before serving. The potatoes will continue to set up as they rest.