To make the pastry put the flour, butter and salt into a food processor and whizz until the mixture resembles breadcrumbs. Add the egg yolk (keep the white) and whizz again until the mixture comes together into a ball. Wrap this in clingfilm and put in the fridge to rest for about 40 minutes.
Cut two of the courgettes into slices about 12mm (½in) thick and grate the rest coarsely. Toss the grated courgettes with 2 tsp salt and put in a colander. Scatter the slices with the remaining ½ tsp and put in another colander (or a sieve). Leave these for 30 minutes.
Roll the pastry out on a lightly floured surface and use to line a 23cm (9in) fluted tart tin (with a removable base). Put in the fridge (or, even better, the freezer) to chill for 15 to 20 minutes (this chilling stops the pastry shrinking when it goes into the oven).
Line the pastry case with crumpled greaseproof paper and baking beans (or dried beans). Put in an oven preheated to 200°C and cook for 7 minutes. Remove the paper and beans and put the pastry back in the oven for 5 more minutes. Lightly beat the reserved egg white, paint it over the base of the pastry and put it back in the oven for 3 more minutes. Remove and leave to cool. Turn down the oven to 180°C.
Dry the courgette slices with a clean tea towel. Put the grated courgettes into another clean tea towel and squeeze out as much water as possible over the sink. Melt half the butter in a frying-pan and sauté the grated vegetables for three minutes then remove. Add the rest of the butter to the pan and sauté the slices on both sides until golden.
Lightly beat the eggs and mix with the cream. Season well and add the parsley.
Spread the grated courgettes in the tart case, scatter over the goat's cheese then put the courgette slices on top (arrange them neatly or higgledy-piggledy, whichever you prefer). Pour on the egg mixture. Bake for 35- 40 minutes or until the tart is puffed up, golden and just set in the middle. Remove and leave to cool. Because the courgette flavour is quite delicate this is best eaten warm or at room temperature, rather than piping hot.