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

Grate the frozen butter using a box grater. Add it to the flour mixture and combine with a pastry cutter, two forks, or your fingers until the mixture comes together in pea-sized crumbs. Place in the refrigerator or freezer as you mix the wet ingredients together.

Whisk 2/3 cup buttermilk and the egg yolk together. (Save egg white for step 5.) Pour over the flour/cheese mixture, add the ham, and then mix until the dough clumps together.

Pour dough onto a lightly floured work surface and, with floured hands, work dough into a ball as best you can. Dough will be sticky. If it’s too sticky, add a little more flour. If it seems too dry, add 1–2 more Tablespoons cold buttermilk. Press into an 8-inch disc and, with a sharp knife or bench scraper, cut into 8 wedges. See recipe Note for smaller scones. To make 10–12 drop scones: Keep mixing dough in the bowl until it comes together. Drop dough, about 1/4 cup of dough per scone, 3 inches apart on a lined baking sheet.

Whisk 1 Tablespoon buttermilk with reserved egg white. Brush lightly onto scones and, if desired, sprinkle with flaky sea salt. (You can do this before or after refrigerating in the next step.)

Place scones on a plate or lined baking sheet (if your refrigerator has space!) and refrigerate for at least 15 minutes.

Meanwhile, preheat oven to 400°F (204°C).

Line a large baking sheet with parchment paper or silicone baking mat(s). If making mini or drop scones, use 2 baking sheets. After refrigerating, arrange scones 2–3 inches apart on the prepared baking sheet(s).

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

Leftover scones keep well at room temperature for 2 days or in the refrigerator for up to 5 days. Scones become softer by day 2.