Preheat oven to 400 degrees.
In a medium bowl, mix together flour, baking powder, baking soda, and salt.
Add the butter and with a pastry blender or your fingers, mix the butter into the dry ingredients until it is crumbly and the largest pieces of butter are no bigger than the size of peas.
Add the shredded cheese and mix, then mix in the buttermilk. Mix just until combined.
Turn out onto a floured surface, or a large piece of parchment.
Press the dough out until it is about 1/2 inch thick, then fold into thirds and press out again to ½ inch thick.
Cut into rounds with a biscuit cutter and place on a parchment lined baking sheet so the edges are just touching.
Gather up any remaining dough and repeat the process of pressing, folding and cutting until no dough remains.
Whisk together the egg and 2 tsp milk and brush over biscuit tops.
Place in oven and bake for 20 minutes until risen and golden.