In a mixing bowl, beat the eggs until frothy - Whisk in the heavy cream, garlic, salt, pepper, and nutmeg - Set aside until needed
Use a mandolin or a very sharp thin knife to slice your potatoes very thin - NOTE: Ideally you are looking for nearly transparent slices about 1⁄16 inch thick but if you do not have a mandolin or the patience/knife skills, ⅛ inch thick slices will work just fine
Grease a 9 ½ inch pie dish with the butter and lay in potatoes in overlapping rows until the bottom of the dish is completely covered (about 4 layers thick if your potatoes are really thin - 2 if thicker)
Sprinkle a small handful of the grated cheese over the top - Drizzle with a bit of the egg/cream mixture
Repeat layering your potatoes in the same manner until about halfway up the depth of the dish – Pour about half of the remaining egg mixture over the top at this layer and jiggle the dish to get it to spread throughout what you have layered - NOTE: You may have to use a fork to lift the layers and then press down to get it well distributed
Repeat layering the potatoes, cheese, and egg/cream mixture until the potatoes and cheese are used up - Pour the remaining egg/cream mixture over the top and, again, jiggle the dish to distribute
Cover with aluminum foil, place on a baking sheet, and bake in the center of the oven for 1 hour 30 minutes - Remove the foil and allow to bake until the potatoes in the center are tender (apx 10 minutes) - Sprinkle with a handful of additional Gruyère cheese and the thyme leaves - Bake for another 5-10 minutes until melted and bubbly
Allow to cool for 15-20 minutes before placing a platter over the top of the dish and carefully overturning the ‘pie’ onto the platter - Slice into wedges and serve warm