3½ cups unbleached all-purpose flour
2½ teaspoons baking powder
¼ teaspoon baking soda
1 teaspoon kosher salt
1 teaspoon sugar
1 cup unsalted butter, chilled and cubed, plus 2 tablespoons, melted
1 cup buttermilk
1½ cups coarsely chopped (1-inch pieces) country ham
8 scallions, sliced into ¼-inch-wide pieces
2 cups grated Cheddar cheese
Preheat the oven to 400 degrees. Line a baking sheet with parchment paper.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, and sugar. Cut the chilled cubed butter into the flour mixture with your fingers until broken down into pea-sized pieces.
Pour the buttermilk into the dry mixture all at once and, using a spoon, fold in the buttermilk quickly and as gently as possible. Add the ham, scallions, and cheese and gently mix until completely incorporated.
Flour your hands and reach into the bowl and under the dough and combine, flipping it around. Mix it up as gently as possible without being too tough on the dough. The dough will be sticky, but manageable. Add more flour if needed.
Turn the dough out onto a lightly floured surface and, working lightly, use your hands to pat the dough into a roughly 8 x 10-inch rectangle about ¾ inch thick.
Dip a 3-inch biscuit cutter into flour and cut as many scones as you can from the dough. Place the scones on the prepared baking sheet and bake for 15 to 20 minutes, turning the pan after halfway through the cooking time, until the tops are light golden brown.
Meanwhile mix the 2 tablespoons melted butter with a pinch of salt.
Transfer the scones to a wire rack and brush their tops with the melted butter. The scones will keep in a tightly sealed plastic bag at room temperature for up to a day or so for best results.