Heat oven to 180C/fan 160C/Gas 4. Heat half the oil in a heavy based ovenproof pan about 23cm in diameter. Add the onion & cook for 2-3 mins until softened,but not browned, stirring frequently. Stir in the courgettes, thyme & garlic, the cook for another 4-5 mins until softened, stirring every now & then, Season to taste. Set aside.
Meanwhile, break the eggs into a large bowl & lightly beat. Add half the parmesan & the basil, & beat together.When the courgettes are cooked, stir them into the egg mixture, the season to taste. Heat the remaining oil in the frying pan, swirling to cover the sides evenly.Tip in the courgette egg mixture & cook for 2-3 minsover a low heat so that the bottom & sides set.
Scatter the remaining pamesan on top of the frittata, transfer the pan to the oven & cook uncovered,for another 10 mins until just set, puffed up & lighlty golden.Loosen the sides with a palette knife & turn out onto a large, warmed serving plate. Cut into wedges to serve.