Combine the flour and salt in a large bowl. Add in the butter and shortening. Using a pastry cutter, gradually work the butter and shortening into the flour until the mixture resembles tiny pebbles. This step should take 3 or 4 minutes.
Lightly beat the egg with a fork, and then add it to the mixture. Next, add in the cold water and vinegar. Stir the mixture together until it's just combined, and then remove half the dough from the bowl.