Preheat the oven to 425 degrees.

Measure the flour and salt into a food processor. Add the margarine and vegetable shortening in chunks. Process ingredients on pulse about 18 times, until the mixture resembles coarse crumbs. Add 3 tablespoons water gradually with the machine on, adding more water only if necessary to form a soft ball of dough.

Wrap the dough in plastic and let rest in the refrigerator for about 30 minutes. When chilled, divide the dough into 8-10 equal pieces and roll each piece into a circle about 1/8-inch thick.

Place the chopped beef, potatoes, onion, peas and carrot, if used, in a bowl and mix well. Season to taste with salt and pepper.

Spoon the mixture evenly just below the center of each rolled out piece of dough. Top each with one piece of margarine. Brush a film of beaten egg around the perimeter of each circle. Gently fold the dough into half circles, covering the filling and crimping the edges together.

Place the pasties on a cookie sheet. Brush the pasties with beaten egg. Bake for 10 minutes. Reduce the oven heat to 375 degrees. Brush the pasties with egg for a second time. Bake for another 25-30 minutes or until golden brown. Remove to a wire rack to cool.