Preheat oven to 400°F. Line a baking sheet with parchment paper.
In a large bowl, whisk together the flour, sugar, baking powder, garlic powder, salt, and black pepper.
Grate the frozen butter with a box grater and add it to the flour mixture. Using a pastry cutter or two forks, work the butter into the flour until the mixture resembles coarse crumbs with pea-sized pieces of butter. Refrigerate the bowl while preparing the buttermilk.
Stir in the chopped chives and shredded cheddar cheese.
Pour the cold buttermilk into the flour mixture and gently stir just until the dough comes together. Do not overmix.
Turn the dough onto a lightly floured surface. With lightly floured hands, gently shape it into a ball, then flatten into an 8-inch circle about 1 inch thick. If the dough feels sticky, dust with a little flour. If it seems dry, add 1 to 2 tablespoons more cold buttermilk.
Cut the dough into 8 wedges using a sharp knife or bench scraper.
Brush the tops with the remaining tablespoon of buttermilk and lightly sprinkle with a pinch of salt.
Arrange the scones on the prepared baking sheet, leaving 2 to 3 inches between each one. Refrigerate for at least 15 minutes while the oven finishes preheating.
Bake for 22 to 25 minutes, or until the tops are lightly golden and the edges are nicely browned. (Mine are perfect at exactly 23 minutes, but every oven is a little different.)
Let the scones cool on the baking sheet for 5 minutes before serving warm.