Place 1 disk of dough on a floured work surface. With a floured rolling pin, roll the dough into a 13-by-10-inch rectangle. Repeat with a second disk. Fit the 2 rectangles, crosswise, in a 15 1/2-by-10 1/2-inch jelly roll pan or on a cookie sheet, overlapping slightly in the middle. (The dough will hang over on all sides.) Roll the third disk into a 15 1/2-by-10 1/2-inch rectangle and place on a cookie sheet lined with parchment or wax paper.
Refrigerate the piecrusts until chilled, at least 30 minutes.
Combine the cherries, cranberries, granulated sugar, cornstarch, ginger, and salt in a large bowl. Pour the mixture into the chilled bottom piecrust and dollop with the butter. Top with the remaining piecrust, centered over the top. Fold the overhanging bottom dough over the top dough and pinch to seal. Brush with the cream and sprinkle with the turbinado sugar. Cut 3 small slits in the top of the pie using a paring knife.
Bake until the juices are bubbling and the crust is golden brown, 1 hour, 20 minutes to 1 hour, 30 minutes.
Serve warm or at room temperature.