Grate the courgettes into a colander. Sprinkle lightly with salt and leave for at least 1 hour to drain. Squeeze out the remaining liquid.
Place the remaining ingredients, except the eggs and olive oil, in a mixing bowl and add the courgettes. Season lightly, bearing in mind you have already salted the courgettes, and mix well. Add the eggs and mix again to combine.
Heat half the olive oil in a large frying pan over a medium-high heat. Place dessertspoonfuls of the mixture, well spaced, in the pan and press down with the back of the spoon. Cook for 1–2 minutes on each side, until golden and cooked through. Remove from the pan and keep warm. Repeat to cook the rest of the fritters in the same way, adding the remaining oil to the pan when necessary.