Preheat oven to 200 C / Gas 6. Grease a 20cm (8 in) loose base tart tin 2.5cm (1 in) deep.
For the pastry:
In a food processor combine the flour and butter, a pinch of salt and cayenne. Blend until mixture resembles breadcrumbs. Add the grated Parmesan or Cheddar cheese and 1 egg, then pulse until combined. Add a little cold water, if necessary. Cover and chill in the fridge for 20 minutes.
Roll out the pastry and press into the prepared tin and prick the bottom.
Line the pastry with baking parchment and fill with baking beans.
Bake blind for 15 minutes in preheated oven. Take out of the oven and remove paper and beans.
Bake for a further 5 to 10 minutes.
Lightly whisk 1 egg and use to brush the inside of the pastry shell.
Bake for 1 minute. Remove from oven and reduce oven temperature to 180 C / Gas 4.
For the filling:
Mix the remaining 2 eggs with creamy goat's cheese, crème fraîche and chives. Season with pepper and nutmeg. Crumble the hard goat's cheese into the egg mixture and pour into pastry shell.
Bake for 25 to 30 minutes, until set. Cool 5 minutes before taking from tin.
You can freeze the cooked tart. Reheat for 20 minutes at 200 C / Gas 6.
Parmesan cheese is not truly vegetarian, as it contains animal rennet. To make this dish 100% vegetarian, omit the cheese or find a suitable vegetarian substitute made without animal rennet. In supermarkets look for the 'parmesan style hard cheeses' which are suitable for vegetarians.