Wash the mallow very well several times in a large bowl of water. Drain thoroughly. Finely chop the leaves, place them in a steamer, and steam over simmering water for 15 to 20 minutes, until the leaves darken and are tender.
Squeeze out any excess liquid from the steamed mallow, and transfer the mallow to a skillet. Add the remaining ingredients (except for the olives), stir to mix, and saute over medium heat for 5 to 10 minutes until the parsley is wilted and the flavors have blended. Adjust seasoning if desired.
Serve warm or at room temperature, garnishing the salad with the olives and preserved lemon rinds.