Preheat the oven to 385°F (195°C).
Using a mandoline slicer, slice the zucchini lengthwise into very thin slices, about 1 mm thick.
In a large shallow plate, combine the chopped basil, chopped mint, panko breadcrumbs, salt, and black pepper. Mix everything together.
Arrange the zucchini slices on a clean work surface and lightly brush both sides with olive oil.
Press each zucchini slice into the breadcrumb mixture to coat both sides.
Place the coated zucchini slices on your work surface. Top each one with a slice of cooked ham, followed by a slice of scamorza cheese.
Roll up each zucchini slice with the ham and cheese inside.
Line a baking dish with parchment paper and lightly brush it with olive oil. Place the zucchini rolls upright and close together so they don’t fall over while baking.
Drizzle a little olive oil over the zucchini rolls and sprinkle the tops with grated mozzarella.
Bake for about 25 minutes, until the zucchini is tender and the tops are golden.