Brush the tortillas with oil on both sides and season 1 side with salt, pepper and cumin. Place on a baking sheet and bake until lightly golden brown. When cool enough to handle, cut into eighths or break into chip-size pieces.
Preheat the grill to high. Grill the eggplant until soft, about 25 to 30 minutes. Let cool slightly, cut each in half, and remove the flesh and place it in the work bowl of a food processor. Add the remaining ingredients and process until smooth. Season with salt and pepper, to taste. Scrape the mixture into a serving bowl, garnish with additional chopped cilantro, and serve with the baked tortilla chips.