Preheat oven to 425 degrees. Line a baking sheet with a silicone baking mat or parchment paper.
In a large bowl, whisk together the flour, sugar, baking powder, and salt. Set aside.
Grate the frozen butter using a box grater. (can also use a food processor)
Toss the grated butter into the flour mixture and combine it with a a fork, or your fingers until the mixture resembles large crumbs. Set aside.
Using a wooden spoon, stir in buttermilk, cheese, ham and chives until a soft dough forms.
Working on your prepared baking sheet, knead the dough a couple of times until it comes together.
Using a rolling pin, roll the dough into an 8-inch circle, about 1-inch thick, and cut into 8 wedges using a sharp knife or pizza cutter.
Place into oven and bake for 18-20 minutes, or until firm to the touch and lightly browned.
Remove and serve immediately.