Filling.
First a vegetarian version. Peel and slice one potato and three carrots. Fry in hot olive oil until beginning to soften. Add one finely chopped onion and one packet of Yves Veggie Ground Round (the Mexican version is good for this). Add 1/2 cup of red wine to deglaze the bottom of the pan and allow to thicken slightly. Set aside for filling the pastry.
A traditional Cornish pasty contains beef, onion, and turnip (swede if in Cornwall) and he strongly flavored with pepper. Lots of variations are possible. You can cook this filling in a frying pan as with the vegetarian version, or you can place it uncooked into the pastry and simply bake for longer.
Pastry
Hot water crust pastry is very easy to make and fun to work with. I used 2 cups of white bread flour, 1/2 teaspoon of salt mixed in a bowl. Take 100ml of cold water and place in a small pan. Add 4 ounces of fat, with large being the traditional ingredient and which seems to work the best. Vegetable shortening can certainly be used instead. Heat the pan until the water boils and the fat melts. Pour this while boiling hot onto the flour and salt, and mix with a fork. You may need to add some more hot water up to the point at which the dough will stick together when pressed between the fingers. Allow this to cool a little if it is too hot to handle, but if your hands are comfortable with the temperature it's okay to place it on your work surface and start kneading. You will need very little flour for this, as the dough is a bit greasy and does not tend to stick to things. Unlike short crust pastry, this kind of benefits from being handled. Knead it until it is consistent and soft. It should resemble Play-Doh in texture and elasticity. Roll it out to 1/4 inch thickness and cut into 6 - 8 inch circles - I use the lid of a metal biscuit tin as a cutter. Hot water crust pastry can be used for other purposes, and is especially useful for raised pies; the Play-Doh like quality of the pastry allows you to form it around a mold. It is best known for its use in game pies and traditional English pork pies, where a gelatin broth is poured into the pie after cooking (leave a hole in the lid) and allowed to set.
Build the pasties
There are two ways of doing this. You can hold the circle of dough in the palm of your left hand, place about 1 1/2 dessert spoons of filling in the center of the circle and then fold the edges up, pinching them together in a ridge. Having a cup of water at hand to wet the edges will help them stick. The other design is achieved by leaving the circle of dough on a flat surface, adding the filling into one side, then folding the other side of the circle over the top of the filling and again pinching and sealing the edge. If you have an egg to spare, this can be beaten and painted onto the pastry which will give it a glossy surface.
Bake
Place the pasties onto a greased baking tray (or one with a silicone mat) and put into a preheated 350° oven for 45 minutes in the case of the vegetarian filling, but for 50 to 60 minutes for the meat filling. My preference would be to pre-cook the meat filling to be certain to avoid serving undercooked meat. Allow to cool a bit before serving.
These will keep in the fridge and can be re-warmed and can be frozen (but be careful as the pastry may crack). The two different designs can be seen in this photograph:

Chris