Preheat oven to 375ºF (190ºC)with rack set in middle position.
Heat 2 tablespoons olive oil in a 10-inch cast iron skillet over medium-high until shimmering. Add ¼ cup packed sage leaves and fry until crisp and starting to brown, 3–5 minutes. Using a slotted spoon or cooking tweezers, transfer leaves to a paper-towel-lined plate. Pour excess oil into a heat proof bowl (do not scrape the pan clean thought); set oil aside.
Using a large-hole grater, shred 8 ounces Gruyère cheese; set aside.
Using a mandoline, thinly slice 2 pounds potatoes to ⅛-inch thick; transfer to a large mixing bowl. Add ¼ cup flour, 3 minced garlic cloves, and ¼ teaspoon nutmeg to potatoes; toss to combine. Add 1 teaspoon kosher salt and 1 teaspoon black pepper; toss to combine.*
Layer ⅓ of potatoes in cast-iron skillet (this will be about 3 layers of potatoes). Sprinkle ⅓ of cheese over potatoes. Layer another ⅓ of potatoes followed by another ⅓ of cheese. Repeat layering once more with reminiang potatoes and cheese.
Pour ¾ cup half-and-half over potatoes, distributing evenly. Drizzle reserved sage oil over top. Tightly cover skillet with foil and bake 30 minutes. Remove foil, increase oven temperature to 400ºF and bake until deply golden brown, 25–30 minutes. Crush fried sage over top and serve.