Sesame-Ginger Chicken Noodle Soup

toasted sesame oil, plus more for serving

bone-in, skin-on chicken breasts (about 1 1/2 pounds)

Kosher salt

(2-inch) piece fresh ginger, sliced, plus extra julienned ginger, for garnish

rice cooking wine or any type of white wine

fresh ramen noodles or 8 ounces dried ramen noodles

scallions, thinly sliced

Ground white or black pepper, for serving