Sprinkle garlic salt over both sides of eggplant slices; let sit for 30 minutes to release water.
Place eggplant slices in a large dish; drizzle with fish sauce. Add basil, balsamic vinegar, and olive oil; stir to evenly coat. Marinate for about 15 minutes.
Preheat grill for medium heat and lightly oil the grate.
Remove eggplant from marinade and arrange on preheated grill; cook until tender, occasionally basting with marinade, about 5 minutes per side.
