Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper.
In a large bowl, whisk together the flour, sugar, baking powder, salt and black pepper.
Grate the cold butter into the flour mixture, or cut it into small cubes and work it in with a pastry cutter. Stop when the mixture resembles coarse crumbs with small pieces of butter remaining. Stir in the cheddar cheese and green onions.
Beat the egg in a small bowl, then divide it equally between two bowls. Whisk one half with the cold buttermilk. Reserve the other half for brushing the scones.
Pour the buttermilk mixture into the dry ingredients. Stir gently with a fork until a shaggy dough forms. Avoid overmixing.
Turn the dough onto a lightly floured surface. Gently bring it together with your hands, then pat into a disk about 1 inch thick. Cut into four equal wedges.
Place the cheddar and green onion scones on the prepared baking sheet, leaving about 2 inches between them. If the butter has softened, refrigerate the wedges for 10 minutes before baking.
Mix the reserved beaten egg with 1 teaspoon of water. Brush a thin layer over the tops, avoiding the cut sides. Discard any leftover egg wash.
Bake for 22–25 minutes, until the tops and bottoms are golden and the centres are set. If the tops brown before the centres finish baking, cover loosely with foil.
Transfer to a wire rack and let cool for 5 minutes. Serve warm, with butter if desired.