Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper.
In a large mixing bowl, whisk together the flour, baking powder, and salt.
Add the cold butter pieces and use a pastry cutter to cut the butter into the flour mixture until it resembles coarse crumbs.
Stir in the shredded cheddar cheese and chopped chives.
Pour in the milk and stir until just combined. Do not overmix.
Turn the dough out onto a lightly floured surface and knead gently a few times until it comes together.
Pat the dough into a 1-inch thick round. Use a biscuit cutter or a knife to cut out scones and place them on the prepared baking sheet.
Brush the tops with the beaten egg.
Bake for 18-20 minutes, or until the scones are golden brown.
Let cool slightly before serving. Enjoy!