Preheat the oven to 450 degrees F. and grease or spray a cast-iron skillet with cooking spray.
In a medium bowl, whisk together the all-purpose flour, baking powder, sugar, cream of tartar, and salt. Set aside.
In a separate small bowl, whisk together the egg, milk, cheddar cheese, and chopped fresh herbs. Set aside.
Using a fork or pastry cutter, cut the cubed cold butter into the flour mixture until it resembles a coarse meal and the butter is about the size of a pea.
Mix the egg mixture into the flour mixture using a wooden spoon until it comes together to form a loose dough ball.
Roll the dough into a ball, flour a clean work surface, and then using a rolling pin. Roll out the dough and cut the biscuits using a biscuit cutter or anything with a round shape.
Place the cut biscuits into the prepared pan and bake for 10 to 15 minutes, until the tops of the biscuits are golden brown.
Brush the tops of the biscuits with additional butter if you would like and serve immediately.