Preheat your grill to medium-high. Toss the eggplant with half the oil; season with salt and pepper. Grill the eggplant 2 to 2 1/2 minutes per side, or until nicely charred and tender. Arrange the eggplant on a platter. Cool to room temperature. Drizzle with remaining olive oil and balsamic vinegar. Top with feta cheese and oregano and serve.