Cook the pasta in a pan of boiling salted water according to the packet instructions, then drain, reserving a mugful of cooking water. Meanwhile, slice the courgettes lengthways, then again into long matchsticks with good knife skills or using the julienne cutter on a mandolin (use the guard!). Place a large non-stick frying pan on a medium-high heat with 1 tablespoon of olive oil, then add the courgettes. Cook for 4 minutes, tossing regularly, while you finely slice the mint leaves, then stir them into the pan.
Toss the drained pasta into the courgette pan with a splash of reserved cooking water. Finely grate in most of the Parmesan and a little lemon zest, squeeze in all the juice, toss well, then taste and season to perfection with sea salt and black pepper. Dish up, finely grate over the remaining Parmesan and drizzle with 1 teaspoon of extra virgin olive oil before tucking in.