In a food processor (or in a large bowl, using a pastry blender, 2 crossed knives, or your fingertips), combine the flour, salt, butter, and shortening until the mixture is crumbly and the size of peas.
Break the egg into a measuring cup and beat lightly; add the vinegar and enough cold water to measure 1/2 cup. Slowly add the egg mixture to the flour mixture and stir until a soft dough forms.
Divide in half. Shape each half into a flat disk and wrap in plastic. Refrigerate for at least 1 hour.