Place the butter in the freezer for 15 minutes. You want it very cold! In a large mixing bowl, add all dry ingredients. Whisk to evenly combine. Set aside.
Remove butter from the freezer and grate it on the large side of a box grater. Add to large mixing bowl and using your hands or a fork, quickly mix it into the flour mixture.
Add the shredded cheeses and blackberries to the flour mixture. Use a fork to stir everything together. Place the bowl in the refrigerator or freezer.
Separate the egg, and add the egg yolk to a glass measuring cup or bowl. Set the egg white aside for later. Whisk the buttermilk into the egg yolk until fully combined.
Pour the buttermilk/egg mixture into the bowl of dry ingredients. Mix together until a shaggy dough is formed. Be careful not to over mix!
Gently turn the dough on a floured surface until a 5-6” ish disc is formed. Cut into 8 mini wedges. Line a quarter sheet baking pan with parchment paper. Transfer the wedges into the freezer for 20 minutes.
Preheat the oven to 400°F (200°C). Mix the egg white with a tablespoon of buttermilk. Brush the chilled wedges with the egg white mixture. Bake the scones for 14-17 minutes, until golden brown. Rotate the pan halfway through.