Preheat oven to 200 degrees F. Line a sheet pan with parchment paper. Grip frozen ham end with a paper towel and use the Microplane to finely grate ham over parchment paper. (As much as you can, avoid the fatty parts.) Yields 6 or 7 tablespoons. Bake 1 hour.
After baking, the ham salt will be completely dried out, crispy, and reduced by half. Rub between your fingers to break up any clumps. Transfer ¾ to a bowl to layer potatoes and ¼ for garnish and set aside. (Ham salt can be stored in an airtight container at room temperature.)
Preheat oven to 400 degrees F. Peel potatoes, then slice ⅛-inch thick on a mandoline.
Spread 2 tablespoons bacon fat across the bottom of the cast-iron skillet; cover with a layer of potato slices, slightly overlapping. Season lightly with salt, pepper, and a sprinkle of ham salt. Drizzle about 2 tablespoons of melted butter over the potatoes, then dust with Gruyère. Add another layer of the potatoes and repeat seasoning with salt, pepper, ham salt, butter, and cheese. Continue until the potatoes, butter, Gruyère, and ham salt are used up, about 4 layers, lightly tamping down each layer as you go. When done, drizzle 2 tablespoons bacon fat over the top.
Set the skillet over medium heat. When the potatoes start sizzling (after about 2 minutes), remove from heat and cover the skillet lightly with aluminum foil. Bake 30 minutes, then remove foil and bake another 15–20 minutes, or until a knife can be inserted without resistance.
Run a metal spatula around the edges of the skillet to release the potatoes. Give the skillet a jiggle to make sure the bottom is free. Place a plate over the skillet and invert to transfer. Garnish with remaining Gruyère and ham salt. Serve warm.