Preheat the oven to 450 F and line a baking sheet with parchment paper.

Crack the egg into a 1 cup glass measure and mix well with a fork.  Add the buttermilk to the 3/4 cup mark and mix well again.

In a large mixing bowl, sift the flour, baking powder and salt.  Cut the butter into 1/2" cubes and lightly mix it into the flour mixture with a pastry blender or your fingers until the chunks of butter are the size of peas.  Stir in 3/4 cup of the cheddar (reserve 1/4 cup for sprinkling on top) and stir in the buttermilk until just combined (do not over mix the dough, you want to do this step in more of a tossing motion).

On a lightly floured surface, pat the dough to 1" thick circle and cut with a cookie cutter or sharp knife into 8 pieces.

Place the biscuits on the prepared baking sheet, sprinkle with the remaining 1/4 cup of cheese if desired, and bake for 10-15 minutes until golden brown. Serve warm.