Preheat the oven to 450 degrees F. and line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, baking powder, sugar, cream of tartar, and salt, set aside.
In a separate small bowl, whisk together the egg and milk and set aside.
Using a fork or pastry cutter, cut the cold butter into the flour mixture until it resembles a meal and the butter is about the size of a pea. Mix the in the milk and egg mixture into the flour mixture with a wooden spoon until it comes together to form a dough ball.
Roll the dough into a ball, flour the work surface, and then using a rolling pin roll out the dough and cut the biscuits out using a biscuit cutter. Place the cut biscuits onto the prepared pan and bake for 10 to 15 minutes, until golden brown.
Brush the tops of the biscuits with additional butter if you would like and serve immediately.