Preheat gas grill. Cut eggplant lengthwise into 3⁄8-inch-thick slices. Place 4 tablespoons olive oil into a small bowl. Dip your fingers in oil and quickly spread it onto each slice of eggplant. (Using of your fingers instead of a brush will result in less oil used.) Arrange eggplant slices on a grill rack, and grill until golden, 3 to 5 minutes on each side. Remove and set aside until cool enough to handle.

Arrange a layer of eggplant in the bottom of a dry, sterilized wide-mouthed 1-quart jar with a lid. Sprinkle with some salt, red pepper flakes, garlic and thyme. Continue layering in the same manner until all eggplant, garlic and thyme have been used. Combine remaining olive oil and vinegar and pour it over eggplant layers. Cover the jar with plastic wrap and then cover with the lid. Place in the refrigerator until ready to use, up to 2 weeks.