Pod the broad beans. Blanch in boiling salted water for 1 minute, refresh in iced water and drain. Peel the blanched beans; this will give you about 1 cup of double-peeled beans.
Using a hand peeler, peel the zucchinis into ribbons. Place these in a large bowl with the broad beans. Shred the mint and add to the vegetable mixture.
In another bowl, make a dressing by whisking together the oil, lemon juice, salt and pepper. Dress the vegetables.
Place the ham on a serving platter along with the vegetable salad. Finish with a good grind of pepper and scatter with parmesan shavings.