Preheat the oven to 400˚F. Place garlic cut side up on enough foil to wrap the garlic. Drizzle oil on the exposed surface of the garlic. Wrap the sides up and place the foil wrapped garlic onto a baking tray. Roast in the preheated oven until golden and soft, about 60 minutes.
Set aside to cool, then squeeze the roasted garlic cloves out of the head of garlic into a large mixing bowl. Use a fork to mash the garlic into a paste.
Meanwhile, add ghee to a 10-inch oven safe skillet (preferably coated cast-iron) and melt over low heat. Add thyme leaves and let infuse for about 30 seconds.
Reserve 1 to 2 tablespoons of the melted ghee in the skillet, and scrape the rest into the bowl with the garlic and mix to combine. Add the potatoes, salt and pepper and use your hands to make sure each slice of potato is coated in ghee, garlic and seasoning.
Make sure your skillet is evenly coated in ghee, add more as needed all over the bottom and sides of the skillet. Once the potatoes are evenly coated in the ghee and garlic mixture, start layering them in a concentric circle to fully fill the bottom of the skillet. This first layer will be what everyone sees when you serve, so take a little more care with this. Continue layering the potatoes until you have used them all, then cut a piece of parchment to fit on top of the potatoes. Use an oven safe lid or a smaller skillet on top of the parchment to weigh the potatoes down.
Transfer the potatoes to the oven and roast for about 60 to 65 minutes or until the potatoes are tender and you can insert the tip of a paring knife with no resistance.
Let the potatoes cool in the skillet for about 15 minutes, then very carefully invert the potatoes onto a serving platter. Garnish with thyme leaves and flaky salt, if desired. Cut into wedges and serve.