Pulse the flour, baking powder, sugar and salt in a food processor. Add the shortening and one-third of the butter; pulse until the mixture looks like coarse meal. Add the remaining butter and pulse until it is the size of peas. Add 1/4 cup ice water and pulse a few more times. If the dough doesn't hold together when squeezed, add more ice water, 1 tablespoon at a time, pulsing.
Divide between 2 sheets of plastic wrap. Pat into disks; wrap and chill at least 1 hour.