Preheat oven to 180 C. Beat the sugar and butter until light and fluffy, using an electric mixer. This will take 2 - 3 minutes. Sift in the flour and add in the ground almonds. Using a spatula bring everything together into a soft dough. Don't use your hands or mixer for this part as it will make the dough greasy and the end results won't be so good. Gently use your hands to bring the dough into a ball and then divide the ball into 3 equal pieces. Place each piece on a baking sheet (see note below) and then using your knuckles gently press the dough down to make a flat disc. Don'tuse too much pressure. The disc should be even all around but will still have the indentations from your knuckles. I'm guessing the diametre of each disc will be about 18cm and the disc will be very thin- (this is one of the secrets!) but not see through and there shouldn't be any holes. Using a lightly floured fork, go around the edges and crimp evenly all the way around. Make a few prick marks on the surface of the disc as you would a pie crust. Repeat the process with the other two pieces each on a separate baking sheet.
Place the trays in the oven and bake at 180 for about 15 minutes, watching carefully that the edges don't burn. If the edges start to look too brown, turn the heat down to about 160. It's important to keep the heat high for at least 10 minutes to allow the shortbread to set. After this time, you can lower the heat to gently crisp it up but do keep an eye on it as it can burn. The baking time will be somewhere between 20 - 35 minutes depending on your oven.
When the shortbread is golden all over remove it from the oven and sprinkle it liberally with some golden caster sugar. Leave it to stand for a few minutes and then using a sharp knife cut each disc as you would a pie, into 6 triangular wedges. The finished shortbread should be quite light and crispy. If it is a bit doughy or tastes of raw flour put it back in the oven for a few more minutes to dry out. Once baked the shortbread will keep for about a week (this is a lie, it won't make it till the end of the day) in a tin. You can also freeze it.
Muriel recommends using really thin rimless baking sheets. I bought some really cheap (99p) flimsy ones from Sainsbury's which work very well.
Golden caster sugar gives the shortbread a nice colour. If you haven't got this you can use ordinary caster sugar. For our American friends caster sugar is fine sugar. (not icing sugar!)
The shortbread is quite delicate, so don't worry if it breaks up and you end up with little bits. It will still taste delicious.