Purée vegetables in a food processor along with cilantro, parsley, arugula, vinegar, preserved lemon, and remaining 1/2 cup oil until smooth; season with salt and pepper.
To serve, place 1 cuparugula on each of 4 plates and top with 2 melon wedges and 1/4 of the onion - mint mixture; sprinkle with equal amounts of feta, top with about 6 shrimp, and garnish with some of the remaining fresh mint.