Preheat the oven to 200 degrees. Peel the parsnips and cut them into uniform fries. Place them in a bowl and toss thoroughly with a tablespoon of olive oil, the fresh thyme, pepper, and a pinch of Celtic sea salt. Spread the parsnips over a baking sheet, preferably on parchment paper, so they lie in a single layer and can cook evenly.
Slide the baking sheet into the hot oven and roast the parsnip fries until golden brown, about 25 minutes. Meanwhile, prepare the meat by sprinkling the lamb chops all over with pepper and Celtic sea salt. Heat the tablespoon of ghee or coconut oil in a skillet over high heat. Place the lamb chops in the hot pan and cook them about 3 minutes per side until they are nicely browned and medium-rare.
Remove the meat from the pan immediately once it reaches the desired doneness. Place the lamb chops on a cutting board or plate and loosely cover them with aluminum foil. Let the meat rest for a few minutes so the juices can redistribute throughout. At the same time, remove the roasted parsnip fries from the oven.
Divide the handful of mixed green salad over the plates and drizzle with a few drops of olive oil if desired. Scoop the hot parsnip fries alongside. Finally, place the rested lamb chops on the plates and serve the dish immediately.