Preheat your oven to 425°F (220°C). Line two baking sheets with parchment paper or silicone baking mats.
In a large bowl, whisk together the flour, salt, baking powder, cream of tartar, and sugar.
Grate the cold butter using the large holes of a box grater and toss it with the flour mixture.
Using your fingertips or a pastry cutter, work the butter into the flour until the mixture resembles fine crumbs.
In a small bowl, combine the cream and egg, beating with a fork until well blended.
Pour the cream mixture over the flour-butter mixture and gently mix with your hands until a rough, shaggy dough forms. It should be slightly sticky. (If the dough is too loose, add a bit of flour; if it’s too dry, add a bit more cream.)
Knead the dough lightly four or five times on a floured surface, then pat it into a flattened disk about 1/2 inch thick. Using a biscuit cutter, cut nine circles and place them on the prepared baking sheets, spacing them out to allow for even browning. You may need to re-form the dough and cut again to use up all the dough.
Bake for 15 to 20 minutes, until golden in spots, rotating the baking sheets halfway through. Cool on a rack before serving. The shortcakes can be made a day ahead.