Preheat the oven to 375 F.
Grease an 8″ x 8″ casserole dish with butter.
Whisk the half and half, minced garlic, salt, pepper and nutmeg in a medium bowl. Taste for seasoning and adjust as necessary.
Add the sliced potatoes to the bowl to soak briefly.
Add a thin layer of the half and half mixture to the prepared casserole dish. Add two layers of the sliced potatoes to cover the bottom of the dish followed by a second drizzle of the half and half mixture.
Sprinkle approximately one quarter of the grated cheeses on top. Alternate additional layers of potato, half and half mixture and cheeses until the casserole is nearly full (leaving about 1/2″ of space at the top of the dish; typically about four layers).
Drizzle some heavy cream over the top layer, dot with the diced butter and finish with any remaining cheese.
Cover the casserole dish tightly with foil, place on a sheet pan and transfer to the preheated oven. Bake for 1 hour. Carefully remove the sheet pan from the oven, remove the foil and bake an additional 15 minutes, or until the top is golden brown and bubbly.
Rest briefly, then cut and serve.