Combine the flour, sugar, and salt. There are many ways to cut the butter and shortening into the flour, but I prefer to use a combination of my food processor and my hands. The food processor breaks up the fat quickly, so there is less time for it to get warm. Put the butter in the machine in 3 parts and pulse 2-3 times. By the time you've added all of the butter, some of it will be completely blended into the flour and some will be in large pea-sized pieces. Add the frozen shortening and pulse until it too is pea-sized pieces (it is much softer, so it breaks down quickly). Add the ice water to the dough 3 tablespoons at a time and pulse just once to combine. If you pulse too much at this point you will continue to break down the butter too much.
Once you’ve added all of the water pour the dough out onto the counter, or into a large flat bowl (pasta serving bowl works well). It may still need some water, so I like to do the rest by hand so that I don’t break down the butter too much.
First, try pressing the dough together to determine if it is too dry. If it isn't holding together, or there is still powdery flour then sprinkle a couple more tablespoons of water evenly over the dry spots and try pressing together again. Fold the dough several times over itself with a bench scraper. The dough should come together without falling apart, but not be too mushy with water.
Press into a log and cut into 2 pieces. Form the dough into two disks and wrap it with plastic. Chill for at least 1 hour, but this can be done the day before, or put it in the freezer for a couple of weeks (Allow to defrost overnight in the refrigerator, not the counter or it will be too soft).