1In a small saucepan over medium heat, combine 1/3 cup water, the rice vinegar, and sugar. Bring to a boil, stirring until the sugar dissolves. Remove from the heat, add the shallots, chile, garlic, fish sauce, and lime juice. Let cool completely. Refrigerate until ready to use, at least 30 minutes, and up to 3 days.
2Prepare a charcoal or gas grill for medium heat, or heat a stovetop grill. Oil the grill. Brush the eggplant slices with oil and season with salt. Grill the eggplant slices, turning once, until nicely grill-marked and tender.
3Cut the eggplant into smaller pieces and add to a shallow serving bowl. Toss with the mint and cilantro and drizzle with some of the dressing. Serve warm.