Cut the butter and shortening into a small dice, then place them in the freezer while you prepare the rest of the ingredients. Place the all purpose flour, whole wheat pastry flour, salt, and sugar in the bowl of a food processor fitted with a steel blade, then pulse a few times to combin. Scatter the butter and shortening pieces over the top. Pulse 8 to 12 times, until the butter is the size of chickpeas. Some of the pieces will be small and others will be larger (about the size of a thumnail).
With the machine running, add 4 tablespoons ice water to feed tube. Add the remaining water one tablespoon at a time, just until the dough is moist enough to hold together with a small portion is pinched between your fingers. Pulse the machine until the dough forms a shaggy ball. Place the dough on a lightly floured board and pat into a disk. Wrap in plastic and refrigerate for 60 minutes.
Once chilled, divide the dough in two. Use both immediately or wrap and refrigerate for up to two days or freeze for up to two months.
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