For the shortcakes: Preheat the oven to 400 degrees F. Line a baking sheet with a silicone baking sheet or parchment paper.
In the bowl of a heavy-duty mixer fitted with a paddle attachment, combine the flour, granulated sugar, baking powder and salt on low speed. Add the butter and mix on low until the mixture resembles coarse meal, about 2 minutes. Add the cream and milk and increase the speed to medium; mix until the dough comes together. Remove the dough to a lightly floured surface, lightly knead a few times and shape into a rectangle about 3/4 inch thick.
Cut out dough circles using a 3-inch round cutter. Place the circles on the prepared baking sheet. Brush the tops lightly with cream and sprinkle with the turbinado sugar. Bake until the shortcakes are golden brown, about 20 minutes. Transfer to a rack to cool.
For the strawberries: Meanwhile, place the strawberries in a bowl. Add the granulated sugar and toss together.
To serve, halve the shortcakes horizontally with a serrated knife. Place the bottom halves on individual serving plates, top each with a dollop of whipped cream and then some berries. Cover with the tops of the shortcakes and serve.
The shortcakes can be stored in an airtight container for up to 2 days.