Place eggplants in a 12- by 15-inch baking pan; pierce each several times with a sharp knife. Bake in a 400° regular or convection oven until very soft when pressed, 40 to 50 minutes. Let stand until cool enough to handle, about 15 minutes. Cut off and discard stems; slice eggplants in half lengthwise. With a fork or your fingers, remove flesh in long shreds. Discard peels.
Meanwhile, in a bowl, mix sesame oil, soy sauce, rice vinegar, and garlic. Add eggplant and mix gently to coat. Cover and chill at least 30 minutes or up to 4 hours.
Sprinkle eggplant salad with green onions just before serving.