Stir together flour and salt in a bowl, a rather large one is good. Add the cut up butter, and the shortening. Break up the butter cubes and coat each piece of shortening in flour, breaking each into two or three pieces. Chill in the refrigerator.
Mix the egg with the vinegar and the measured ice water (with no ice in it) and chill if desired. Add a little vanilla, if using.
When ready to proceed, work the flour into the shortening and butter, between finger tips. Keep the mixture light, by allowing the ingredients to sift through the fingers, lifting them up several times.
Do not overwork the fat, allow some pieces to be like meal, some pieces to be like rice, and some pieces to be like the size of a pine nut.
Add the egg, water and vinegar mixture all at once. Quickly work to a paste. It will most likely need more water, add a little at the time to bring a cohesive paste together. I find that this pastry requires a little more water than some. It is a good paste, but I do not like paste dry and crumbly. I always make them a unit.
Wrap well in cling film, or dredge lightly in flour and place in a gallon sized zip-lock bag. Chill well, or freeze for up to a month. Chill overnight before using. Do not keep made pastry in the fridge for more than two days before using. The liquid reacts with the flour in a negative way, after that time. For directions for rolling paste see, Directions for Rolling and Baking Paste, on my site, if desired.