Preheat your oven to 400°F and line a large baking sheet with parchment paper.
In a large bowl, whisk together the flour, sugar, baking powder, and salt. Using your fingers, work the cold butter into the dry ingredients until it resembles coarse breadcrumbs. Stir in the ham, cheese, and green onions.
In a small bowl, combine the buttermilk and egg. Pour over the flour mixture and stir gently until all the flour is moistened and a soft dough forms.
Transfer the dough to a lightly floured surface. Flatten the dough into an 8 disc about 1 inch thick. Slice into 8 wedges and transfer to the prepared baking sheet.
Bake for 18-20 minutes, or until the tops are lightly browned.