Warm the piadina wraps in a dry skillet over medium heat for 1-2 minutes on each side, until lightly golden brown.
Halve the zucchini lengthwise, then slice into thin rounds. Brush the zucchini slices with half of the olive oil and grill or pan-fry them until lightly browned.
Wash and roughly chop the basil. In a food processor or with an immersion blender, blend the basil, remaining olive oil, garlic, salt, and pepper into a smooth cream. If it's too thick, add a little water or olive oil until you reach the desired consistency.
Spread the basil cream evenly over the piadina wraps.
Arrange the grilled zucchini slices on top of the basil cream, then sprinkle with grated Parmesan cheese.
Fold the piadina in half and serve fresh and warm.
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