Combine flour and sea salt in a large bowl. Mix in butter and shortening with a pastry blender or 2 forks until it resembles coarse meal.
Whisk together egg, vinegar, and 1/4 cup cold water, pour into flour mixture, and stir just until it comes together and starts to form a ball. Add more water, 1 tablespoon at a time, if necessary. Press together with lightly floured hands, and form into 2 flat rounds. Cover with plastic wrap, and chill 1 hour or overnight.