You will need a 71/2 inch (19 cm) diameter fluted quiche tin with a removable base, 11/4 inches (3 cm) deep, very lightly buttered, and a small, solid baking sheet. Pre-heat the oven to gas mark 5, 375°F (190°C) and pop the baking sheet in to pre-heat on the centre shelf. Now prepare the leeks. First, take the tough green ends off & discard them; leave some of the lighter green & then make a vertical split about halfway down the centre of each one and clean them by running them under the cold-water tap while you fan out the layers - this will rid them of any hidden dust and grit. Then slice them in half lengthways and chop into 1/2-inch (1 cm) slices. Next, in a medium-sized frying pan, melt the butter over a gentle heat and add the leeks, shallots and some salt. Give it all a good stir and let them cook gently, without a lid, for 10-15 minutes or until the juice runs out of them. Then you need to transfer them to a sieve set over a bowl to drain off the excess juice. Place a saucer with a weight on top of them to press out every drop. Roll it out into a circle on a lightly floured surface. As you roll, give it quarter turns to keep the round shape and roll it as thinly as possible. Now transfer it, rolling it over the pin, to the tin. Press it lightly and firmly over the base and sides of the tin, easing any overlapping pastry back down to the sides, as it is important not to stretch it. Now trim the edges and press the pastry up about 1/4 inch (5 mm) above the rim of the tin all round, and then prick the base all over with a fork. After that, paint some of the beaten egg for the filling over the base and sides. Now place the tin on the baking sheet and bake for 20-25 minutes or until the pastry is crisp and golden. Check halfway through the cooking time to make sure that the pastry is not rising up in the centre. If it is, just prick it a couple of times and press it back down with your hands. While the pastry case is pre-baking, crumble the goats' cheese with your hands, and then gently combine it with the leeks & shallots in the sieve. Now, in a jug, mix the beaten eggs with the creme fraiche or double cream, seasoning with just a little salt (there is some already in the leeks) and a good grinding of freshly milled black pepper. As soon as the pastry case is ready, remove it from the oven; arrange the leeks, shallots and cheese all over the base. Pour the cream and egg mixture over the top of the cheese, shallots & leeks, then put the tart back on the baking sheet with the oven shelf half pulled out, then gently slide the shelf back in and bake the tart for 30-35 minutes, until it's firm in the centre and the surface has turned a lovely golden brown. Next, remove it from the oven and allow it to settle for 10 minutes before serving. These 10 minutes is important, as it will be much easier to cut into portions. The best way to remove the tart from the tin is to ease the edges from the sides of the tin with a small knife, then place it on an upturned jar or tin, which will allow you to carefully ease the sides away. Next slide a palette knife or wide fish slice underneath and ease the tart on to a plate or board ready to serve, or simply cut it into portions straight from the tin base. Serve for picnics, light lunch with mixed salad and baked potatoes or as finger food for a buffet.