Whisk together vinegar and oil. Brush both sides of eggplant slices with mix.
On medium heat, grill eggplant and peppers for 10 minutes until tender and blackened. Take off the grill. Cool.
Peel and seed peppers. Cut into ¼” strips.
To assemble, place 2 pepper strips on one end of each eggplant slice and top with 2 to 4 arugula sprigs, allowing peppers and arugula to extend beyond both sides of eggplant. Roll the eggplant up and place seam-side down on platter. Season with salt and pepper, to taste.