Preheat oven to 450°F (230°C). Lightly grease a cast-iron skillet.
Using a box cheese grater, grate the frozen butter into pea-sized pieces. Place the grated butter back in the freezer while preparing the dry ingredients.
In a large mixing bowl, thoroughly whisk together the flour, sugar, salt, baking powder, and cream of tartar.
Toss the frozen grated butter into the flour mixture and stir to coat.
In a small bowl, whisk the cold buttermilk and the egg. Pour into the flour mixture.
Stir gently with a spatula just until a sticky, shaggy dough forms. Do not overmix.
Turn the dough onto a floured surface. Knead gently 10 to 15 times to bring the dough together.
Pat the dough out to a 3/4-inch to 1-inch thickness. Use a floured biscuit cutter to cut the dough, pressing straight down without twisting.
Place the biscuits in the greased skillet so their edges are touching.
Bake at 450°F for 10 to 15 minutes until the tops are golden brown.
Remove from the oven and immediately brush with melted butter. Serve warm!