Slice the Zucchini: Trim the ends from both zucchini and carefully slice them lengthwise into thin, even strips about 1/4 inch thick using a vegetable mandoline or sharp knife. You should get 4 to 6 long slices per zucchini.
Salt and Rest: Lay the slices on paper towels, sprinkle lightly with salt, and let them sit for 10 minutes to remove excess moisture. Pat dry with fresh paper towels.
Prepare the Coating Station: In one bowl, combine breadcrumbs and Parmesan cheese; in another, prepare a small dish of olive oil for brushing.
Layer the Filling: On each zucchini slice, place one slice of ham, then top with a small piece of mozzarella, leaving a 1/2 inch border on all sides.
Roll Tightly: Roll the zucchini slice from one end to the other, keeping the filling snug inside; place seam-side down on a parchment-lined baking sheet.
Coat with Crumbs: Brush each roll lightly with olive oil, then sprinkle the breadcrumb-Parmesan mixture generously over the top, pressing gently so it adheres.
Bake Until Golden: Bake at 400°F (200°C) for 20 to 25 minutes until the rolls are golden brown and crispy, and the cheese is fully melted inside.