1 pound flank steak, skirt steak, hanger steak, or flap meat, cut into 1/4-inch thick strips
1/4 cup soy sauce (divided)
1/4 cup shaoxing wine or dry sherry (divided)
2 teaspoons corn starch
1/3 cup low-sodium homemade or store-bought chicken stock
1/4 cup oyster sauce
1 tablespoon sugar
1 teaspoon sesame seed oil
2 medium cloves garlic, finely minced (about 2 teaspoons)
2 teaspoons finely minced fresh ginger
3 scallions, whites finely sliced, greens cut into 1/2-inch segments, reserved separately
4 tablespoons vegetable, peanut, or canola oil
1 pound broccoli florets (about 1 1/2 quarts)