On a small, rimmed baking sheet, toss the asparagus with the Parmesan, oil and 1/8 teaspoon of the salt. Bake until the stalks are easily pierced with the tip of a knife, 8 to 10 minutes. Cool completely.
In a small bowl, whisk together the mascarpone, orange zest and the remaining 1/8 teaspoon salt until smooth and spreadable.
One at a time, fold the slices of ham in half and spread each with 1 teaspoon of the mascarpone mixture. Place one spear of cooled asparagus at one end of the slice and roll the ham around the asparagus. Repeat for the remaining asparagus. Place the rolls on a parchment-paper-lined tray and store in the refrigerator, wrapped in plastic wrap, until ready to serve. Serve chilled.