Begin by mixing the flour, salt, and baking powder in the bowl of a food processor fitted with a metal blade.
Add the shortening and butter and mix quickly with your fingers until each piece is coated with flour. Pulse 10 times, or until the fat is the size of peas.
With the motor running, add the ice water; process only enough to moisten the dough and have it just come together.
Dump the dough out onto a floured board and knead quickly into a ball. Wrap the dough in plastic and allow it to rest in the refrigerator for 30 minutes.