Place a large heavy-bottomed, ovenproof skillet, ideally cast iron, over medium to high heat and heat enough olive oil to thinly coat the pan. Place the Brussels sprouts in the pan, in batches if necessary, cut side facing down, and cook until nicely caramelized, 3 to 4 minutes. Transfer to a baking tray lined with parchment paper, cut side up. Roast in the oven until the sprouts are tender all the way through, about 6 minutes. When the sprouts come out of the oven, throw in the parsley leaves and pickled grapes and gently toss to combine.