Slice the courgettes into rounds roughly 3mm thick. If you have time, spread them on a clean cloth and leave them to sit – ideally in the sun, otherwise any dry place – for an hour, turning after 30 minutes.
In a medium frying pan, heat a couple of thumbs of oil and then, working in batches, fry the rounds until lightly golden. Using a slotted spoon, lift the courgettes on to a kitchen towel to blot.
When drained, layer the courgettes in a bowl, sprinkling salt and tucking ripped mint between each layer and in the gaps.
In a small pan, bring the vinegar, water, garlic and chilli to the boil, and continue to boil for five minutes.
Pour the vinegar mixture over the courgettes, along with three tablespoons of olive oil, either from the frying pan or the bottle. Toss the courgettes, cover, and leave to sit for at least an hour – ideally 24 hours. Taste before serving.