Scallops and chorizo are the biggest-selling appetizer we’ve ever had at our brasserie. I even had complaints from customers when I took the dish off the menu! Try if you can to buy diver scallops that are as fresh as possible.
Preheat the broiler to high. Slice the chorizo into 12 slices, no more than ¼-inch thick. Broil for 3 minutes, turning once, until crisp. Remove from the heat, cover with foil, and set aside.
Season the scallops with crushed sea salt and freshly ground black pepper. Heat the oil in a wide, heavy-bottomed frying pan and cook the scallops over high heat for 40 seconds, turn, and cook for another 40 seconds. Remove from the heat.
Arrange the scallops and chorizo on 4 serving plates. Drizzle the balsamic glaze and spoon the warm juices from the grill over the top. Sprinkle with the arugula and garnish with dill.