Preheat the Oven - Set the oven rack to the middle position and preheat to 375ºF (191ºC).
Prepare the Cream - In a medium saucepan over medium-low heat, add heavy cream, milk, minced garlic, salt, pepper, nutmeg, and thyme. Bring to a simmer, occasionally stirring, about 10 minutes. Remove the thyme and transfer the mixture to a large measuring cup. Cool to room temperature while preparing the potatoes.
Prepare the Casserole Dish - Grease the bottom and sides of an 8-Inch square baking dish with 1 tablespoon of melted butter.
Layer the Potato Slices - Wash and peel the potatoes and cut them into ¼" thick slices. Arrange a third of them in overlapping rows, about four rows in the casserole dish. Whisk and then evenly pour a third of the cream mixture over the top.Repeat two more times with the remaining potatoes. Cut 1 tablespoon of butter into small cubes and arrange them evenly on top.
Bake the Casserole - Cover the dish with foil and place it on a large sheet pan. Bake for 60 to 75 minutes, until potatoes are fork-tender. Remove the foil and broil on high, about 8" from the top of the oven, until the potatoes are browned, about 5 minutes.
Cool Before Serving - Wait 10 minutes before serving. Garnish with parsley and black pepper.
Notes
Potato Substitutions: Other waxy potatoes, like gold (similar to Yukon gold) or red potatoes can be used.
Storing: Cover and store in the refrigerator for up to 5 days. Freeze for up to 1 month.
Reheating: Cover and reheat small portions in the microwave on a high setting in 15 to 30-second increments until hot. Alternatively, cover and bake at 350ºF (177ºC) until hot.