Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Brush eggplant lightly with olive oil on both sides. Stir together remaining olive oil, garlic, and salt in a small bowl.
Arrange eggplant slices on the preheated grill and cook, turning occasionally, until tender and browned, 3 to 4 minutes per side.
Arrange grilled eggplant on a platter. Brush with the olive oil and garlic mixture until eggplant has absorbed the oil. Sprinkle with the chopped basil and parsley and serve.