Prepare the Steaming Setup: Place a steamer basket inside a large stockpot. Pour the sake into the pot along with 1 ¼ cups of water, or enough liquid to come just below the basket. If there isn’t enough liquid, top it up with equal parts sake and water. Bring the liquid to a boil.
Season and Steam the Chicken: Sprinkle the chicken breasts generously with kosher salt on both sides. Arrange the pieces in the steamer basket, making sure they aren’t stacked on top of each other. Lower the heat to a gentle simmer, cover the pot, and let the chicken steam for 25 to 35 minutes, or until the juices run clear when pierced with a knife. Take the pot off the heat and allow the chicken to cool slightly for about 10 minutes.
Make the Sauce: While the chicken steams, combine the soy sauce, orange juice, rice vinegar, lime zest, lime juice, mirin, grated ginger, and garlic in a small bowl. Whisk the ingredients together until smooth. If you prefer, you can mix in some of the steaming liquid for added depth of flavor. Taste and adjust seasoning as needed.
Carve and Garnish: Remove the cooked chicken from the pot and transfer it to a cutting board. Slice the meat away from the bones, then cut it into pieces as desired. Arrange the slices on a serving platter and spoon some of the sauce over them. Scatter the sliced scallions and sesame seeds on top for garnish.
Serving Suggestions: For a different option, shred the chicken instead of slicing it, and serve it in the steaming broth as a soup. Stir some of the sauce into the broth for extra seasoning.