Meanwhile, place a large skillet over high heat and add olive oil. Add remaining onions and season with remaining salt mixture. As onions begin to brown, reduce heat to medium. Cook, uncovered, turning onion slices with a spatula every few minutes until caramelized and fork-tender, about 15 to 20 minutes. Add 1/2 cup water to onions and simmer a few minutes more. (For more flavor, use broth from the brisket pan instead.) Onions may be prepared in advance and reheated.
To serve, transfer brisket to a cutting board. Trim extraneous fat from meat. With a large knife, cut meat across the grain into 1/4-inch slices. Strain braising liquid into a saucepan (discard solids left in strainer) and skim any rising fat from surface.
Arrange sliced meat on a platter. Cover with caramelized onions and ladle some hot braising liquid over. Garnish with parsley sprigs and sprinkle with scallions, if using. Serve remaining juices separately.
Nutrition information per serving:
Calories560Fat30 gSodium2,220 mg
Carbohydrates12 gSaturated fat10 gTotal sugars5 g