Preheat the oven to 180C. Wash the courgettes, cut off the ends, and grate the courgettes. Place the courgette in a bowl, amply salt, leave the bowl in the fridge for 20 minutes, then place the courgette on kitchen paper (to drain).
Butter a deep baking form, spread the shortcrust, and prick several times with a fork.
Whisk the egg with the egg yolk, milk, and cream, season with salt and pepper.
Spread the courgette on the shortcrust, then cover with the egg and milk mix. Sprinkle with caraway and bake for 20 minutes. Remove from the oven, and let cool slightly before serving
