Brine the Pork Chops:
In a large bowl, dissolve the kosher salt and sugar into 4 cups of water. Add the thyme sprig and pork chops, ensuring they are fully submerged. Cover and refrigerate the chops for a minimum of 2 hours or up to overnight. Once ready to cook, remove the chops from the brine and pat them dry before discarding the brine.
Cook the Parsnips:
Preheat your oven to 350°F. In a large pot, bring water to a boil, seasoning it with salt. Once the water reaches a boil, add the parsnips and simmer them until they are tender, roughly 8 to 10 minutes. Drain the parsnips and set them aside to keep warm.
Sear the Pork Chops:
While the parsnips cook, heat olive oil in a large skillet over medium-high heat. When the oil begins to shimmer, carefully place the pork chops in the skillet, searing each side for about 3 minutes or until golden brown. If your skillet is not large enough to accommodate all the chops, work in batches.
Roast the Pork Chops:
Transfer the seared pork chops to a roasting pan or sheet pan, arranging them in a single layer. Roast them in the oven for 10 to 15 minutes, or until an instant-read thermometer inserted into the meat reads 140°F. Once cooked, remove the pork chops from the oven and allow them to rest while you prepare the sauce.
Prepare the Brown Butter Sauce:
Wipe the skillet clean and return it to medium-high heat. Add the butter and let it melt, allowing it to brown slightly. Once the butter has begun to brown, add the sage leaves and dates, allowing them to sizzle for approximately one minute. Season the mixture with freshly ground black pepper and lemon juice, then remove from heat. Taste and adjust the seasoning with additional pepper or lemon juice as needed.
Serve the Dish:
To plate, place a portion of the roasted pork chops and a spoonful of the cooked parsnips onto warm plates. Drizzle the brown butter sauce over the pork and parsnips before serving.