For the shortcake biscuits: Preheat the oven to 375 degrees F. Line a baking sheet with parchment.
In a large mixing bowl, combine the flour, baking powder, granulated sugar and salt. Whisk to combine and evenly distribute the leavening. Add the shortening and butter and toss to coat the fat just a bit with the flour. Using your fingertips, gently work the fats into the flour until the mixture resembles coarse cornmeal with some pea-size chunks of fat.
In a small bowl, whisk together the buttermilk and egg, and add this to the flour mixture. Stir together with a wooden spoon. Then, gently work through the mixture with your hands to separate any wet patches and bring the dough together.
Turn the dough out onto a floured work surface, fold it over a few times and knead gently until it just holds together. Pat the dough into a rough 1/2-inch-tall rectangle. Cut out biscuits with a 3-inch biscuit cutter. Pat the scraps together and cut an additional biscuit. You should have 6 to 8 biscuits. Evenly space the biscuits on the prepared baking sheet. Brush the tops with egg wash and sprinkle with the turbinado sugar. Set aside.
For the roasted plums: Pour the butter into a shallow baking dish and tip from side to side to coat the bottom. Add the maple syrup and orange juice, swirling to "stir" the mixture. Line the baking dish with the plums, flesh-side down.
Bake both the biscuits and plums for about 20 minutes. Remove the biscuits when golden brown. Continue to cook the plums until the juices have thickened, about another 15 minutes. Cool completely before assembling.
For the whipped cream: In the bowl of a stand mixer fitted with the whisk attachment, beat together the cream, confectioners' sugar and vanilla until medium peaks form.
To assemble: Split four of the biscuits horizontally in half; reserve the remaining biscuits for another use (see Cook's Note). Place the bottom of each biscuit on a serving plate. Top with a generous dollop of whipped cream, followed by a few plum slices and their juices. Top with the biscuit tops.
The plum shortcakes can be assembled 2 to 3 hours ahead and refrigerated. The extra biscuits keep well in the freezer. When ready to use, thaw at room temperature and warm in a low oven.