Preheat oven to 375°F. Peel potatoes with peeler. Slice into ⅛-inch thin rounds using mandoline on safe setting into bowl of cold water. Drain and pat dry with clean kitchen towels.
Pour cream and milk into saucepan using measuring cups. Add minced garlic, thyme, nutmeg, salt, pepper from measuring spoons. Heat over medium till barely simmering with wooden spoon, 5 minutes. Remove from heat.
Rub baking dish garlic clove half for flavor. Layer ⅓ potato slices shingle-style across bottom. Ladle ⅓ warm cream mix over using measuring cup till potatoes peek through. Sprinkle ½ cup cheese even with spoon. Repeat 2 more layers, end with cheese top.
Cover dish tight with foil. Bake middle rack 60 minutes till knife slides easy through center, potatoes tender.
Remove foil. Bake uncovered 25-30 minutes more till top golden bubbly brown. Rest 10 minutes on rack for slices to set firm.