Combine the flour, sugar, and salt in the bowl of a food processor and pulse a few times to combine. Add the butter and shortening and pulse until the mixture resembles coarse crumbs. With the machine running, add the water in a slow, steady stream, blending just until the dough comes together. If the dough is too dry, add more water 1 tablespoon at a time.
Shape the dough into a flat disk and wrap in plastic wrap. Chill in the refrigerator for at least 1 hour, or overnight.
Transfer the dough to a lightly floured work surface and roll out to an 11-inch circle. Press the dough into a 9-inch tart pan. Trim any excess dough from around the edge and freeze the crust for 10 minutes.
Combine the cranberries, orange zest, orange juice, sugar, cinnamon, and nutmeg in a large bowl. Pour the mixture into the tart shell and spread evenly. Bake for 45 to 55 minutes, until the crust is golden brown and the filling is soft and thickened. Remove from the oven and let cool completely before serving. Serve each slice with a dollop of whipped cream.