Preheat oven to 375°F. Line a baking sheet with parchment paper.
Whisk together flour, baking powder, salt, and baking soda.
Cut in butter with a pastry blender until pea-sized.
Stir in Cheddar and parsley. Add buttermilk and 2 Tbsp water; knead gently just until combined.
Turn dough onto a lightly floured surface and pat into an 8-inch square. Cut dough into 2-inch squares, then cut squares into triangles.
Place scones on prepared baking sheet. Whisk together egg and remaining tablespoon water; brush over tops of scones.
Bake scones until golden, about 25 minutes.
