Heat the oil in a cast-iron pan, or heavy-bottomed pan over medium-high heat. Place the beef in the pan, breaking up pieces and cook until the moisture has evaporated and beef is browned, about 10 minutes. Stir in the onion and red pepper. Once the onion and red peppers have softened, add the garlic powder, cumin, and cayenne, stir to incorporate. Stir in the parsley, green chile, and lime juice. Remove pan from heat and season with salt and pepper.
For the maple syrup sauce:
Place the lime zest, garlic, salt, 2 tablespoons pepper, maple syrup, and vinegar in a pot and warm over medium heat. Transfer the sauce to a bowl.
For the grilled Japanese eggplants:
Heat a grill to medium heat. Drizzle the oil over the eggplant quarters and season with salt and pepper. Place the eggplant on the grill and cook on all sides. Once the eggplant are tender, place in a pan and coat with the warmed Maple Syrup Sauce; toss to coat.