Peel the apples and pears; slice 1/2 inch thick. Melt the butter in a large skillet over medium-high heat. Add the apples, pears, granulated sugar, brown sugar, ginger and salt. Cook, stirring occasionally, until mostly tender, 20 to 25 minutes (reduce the heat if the skillet looks dry). Remove from the heat and stir in the lemon juice, flour and cinnamon. Let cool to room temperature.
Meanwhile, place a baking sheet in the lower third of the oven; preheat to 450 degrees F. Cut 1 dough round into nine 1/4-inch-wide strips; cut the rest of that round into strips of varying thickness. Weave the 1/4-inch strips into 3 thin braids, 3 strips per braid (these will be for the edges). Make braids with some of the remaining strips; leave some as is. Refrigerate the braids and strips until firm, 30 minutes.
Line a 9-inch pie plate with the other dough round; add the filling. Arrange the dough strips and braids (except for the 3 for the edges) parallel to one another on top of the filling. Trim any excess dough around the edges. Brush the edges with beaten egg and line with the 3 thin braids; trim the excess. Brush all of the dough with egg and sprinkle with turbinado sugar.
Bake the pie on the hot baking sheet, 20 minutes. Reduce the oven temperature to 375 degrees F and bake until the filling is bubbling and the crust is browned, about 1 more hour. (Cover the crust with foil if it darkens too quickly.) Transfer to a rack to cool completely.