Wash and dry the courgettes then trim the ends. Cut them into 1 cm thick slices.
Heat the olive oil in a frying pan large enough to hold the courgettes in one layer. Add the garlic to the oil and, when soft, add the courgettes. Season and stir until just beginning to brown.
Add half the butter, stir and lower the heat. Continue cooking, adding a small amount of water to loosen any bits that stick to the pan. Stir and scrape until the courgettes have become soft and creamy. Remove from the heat and stir in the rest of the butter.
Cook the fusilli in boiling salted water according to packet instructions until al dente. Drain, reserving a little of the cooking water. Stir this into the courgettes to loosen the sauce.
Add the pasta to the sauce and toss very well. Serve with the grated Parmesan.