Whisk together vinegar and oil. Brush both sides of eggplant slices with ¼ cup oil mix. Grill eggplant on medium heat until cooked through. Brush with remaining oil mix & turn occasionally (approx. 4 minutes). Remove from grill. Cool.
Grill bell peppers until blackened on all sides. Remove from grill and let stand 10 minutes. Peel and seed peppers. Cut into ¼” strips.
Place 2 pepper strips on 1 end of each eggplant slice; top with 2 to 4 arugula sprigs, allowing peppers and arugula to extend beyond both sides of eggplant. Roll eggplant up. Place seam-side down on platter. Season with salt and pepper.