Heat 2 teaspoons of oil in a nonstick pan.
Add the garlic and zucchini and sauté over mediumâhigh heat until lightly golden, shuffling them with a wooden spoon so that they cook evenly.
Season with salt and mix in the basil. Remove from the heat and remove the garlic.
Whisk one egg in a bowl.
Heat 1 teaspoon of oil in a 6-inch nonstick frying pan over mediumâlow heat. Add the egg, swirling it evenly around the pan.
Scatter about a quarter of the zucchini over the omelet and about 1½ tablespoons of parmesan.
Cook until the omelet is set and the underside is lightly golden.
Slip out onto a warm plate while you make the rest, adding more oil to the pan as needed.
Serve with a few drops of lemon juice and a grinding of pepper, if you like.