Cut the courgette into long, thin slices, then brush with oil and grill them in a griddle pan or under the grill.
Lightly toast the pine nuts, then set aside.
Meanwhile, put the spinach, garlic, lemon juice, cheese, basil and most of the pine nuts in a food processor. Pulse for a few seconds.
Add the courgette slices and pulse until you get a textured paste. Season to taste.
Transfer the pesto to a small bowl. Scatter the remaining pine nuts on top and add some grated cheese.
Cover and keep refrigerated, then use it up within 3 days.