Cut the two ends off the eggplant and slice lengthwise into 1/4 inch slices (or into rounds). Salt the slices to help remove excess moisture and any bitterness from the eggplants and place in a colander. Set aside for about 15 minutes.
Rinse the salt off the eggplant with cold water and pat dry with paper towels. Preheat the grill to medium or heat a grill pan on the stove top over medium-high heat. Make sure it's hot before beginning. Using a pastry brush, lightly brush both sides of each slice of eggplant with the olive oil and sprinkle with salt and pepper. Grill on both sides until you have nice grill marks and the eggplant is pliable, about 3-4 minutes on each side.
In a small jar with a lid, combine the olive oil, lemon juice, vinegar, honey and garlic. Cover and shake until mixed well. Taste, and add salt and pepper as needed.
Cut the grilled eggplant into bite-size pieces and toss with a bit of prepared dressing. Top with the parsley, mint, pomegranate arils and feta cheese. Drizzle with the remaining dressing, toss gently to coat. Enjoy!