How to Make It
Preheat oven to 425°F. Line a baking sheet with parchment paper; set aside.
Whisk together flour, sugar, baking powder, dry mustard, and salt in a large bowl. Using a pastry blender or 2 knives, cut butter into flour mixture until mixture resembles corn kernels. Fold cheese, ham, and chives into mixture. Add buttermilk and 1/4 cup of the cream, and stir just until mixture comes together.
Sprinkle parchment-lined baking sheet liberally with flour. Divide dough in half. Place 1 dough half on prepared baking sheet; cover and chill remaining dough half. With floured hands, shape dough into an 8-inch slanted rectangle (about 1 inch thick). Brush evenly with 1 tablespoon of the heavy cream. Sprinkle evenly with 1/4 teaspoon of the pepper. Using a floured bench scraper or knife, cut dough square into 8 slanted squares (rhombuses). Carefully pull scones away from center to separate them by about 3/4 inch.
Bake in preheated oven until golden brown and cooked through, 15 to 18 minutes. Repeat with remaining dough half, cream, and pepper. Serve warm or at room temperature.
Note: Scones can be cut in advance, and frozen on a baking sheet. Once they are completely frozen, transfer scones to a ziplock plastic freezer bag for longer storage. Bake directly from frozen. You may need to add a couple of minutes to the baking time.