In a large bowl, whisk together the flour, sugar, baking powder, garlic powder, salt, and black pepper. Stir in the chives and shredded cheddar cheese.

Grate the frozen butter using a box grater and add it to the flour mixture. Use a pastry cutter, two forks, or your fingers to combine until the mixture resembles pea-sized crumbs. Place the bowl in the refrigerator or freezer while you prepare the wet ingredients.

In a separate bowl, whisk together ⅔ cup of buttermilk and the egg yolk (set aside the egg white for later). Pour this mixture over the flour and cheese mixture, add the chopped ham, and mix until the dough clumps together.

For triangle scones: Transfer the dough to a lightly floured work surface. With floured hands, shape the dough into a ball. If the dough is too sticky, add a little more flour; if too dry, add 1-2 tablespoons of cold buttermilk. Press the dough into an 8-inch disc and cut into 8 wedges. For drop scones: Keep mixing the dough in the bowl until it comes together. Drop about ¼ cup of dough per scone onto a lined baking sheet, spacing them 3 inches apart.

In a small bowl, whisk together 1 tablespoon of buttermilk and the reserved egg white. Brush this mixture lightly over the scones and sprinkle with flaky sea salt if desired. You can do this step before or after refrigerating the scones.

Place the scones on a plate or lined baking sheet and refrigerate for at least 15 minutes.

Preheat your oven to 400°F (204°C). Line a large baking sheet with parchment paper or silicone baking mats. If making mini or drop scones, use two baking sheets. After refrigerating, arrange the scones 2-3 inches apart on the prepared baking sheet(s).

Bake for 22-25 minutes, or until the scones are golden brown around the edges and lightly browned on top. Remove from the oven and let cool for a few minutes on the baking sheets before serving.