Grease the bottom of the medium casserole pan with melted butter.
Spread ¼ of the sliced potatoes in an even layer on the bottom of the pan. Sprinkle the potatoes with ⅛ teaspoon salt, then top with 1 minced garlic clove, ¼ cup of grated Parmesan cheese, ¼ amount of thyme leaves (removed from sprigs). Top with ¼ cup of heavy creamy, pouring it evenly over the potatoes.
Repeat layers 3 more times (total of 4 layers of potatoes). For the last layer, use ½ cup of shredded Parmesan cheese (or more).
Bake at 400 F, uncovered, for about 1 hour, or until the potatoes are cooked through.