Preheat oven to 450°F. Line a baking sheet with parchment paper. Set aside.
In a large mixing bowl, use a whisk to sift together flour, baking powder, baking soda and salt.
Add grated butter, mix until evenly distributed.
To the bowl add ham, cheese and chives, mix well until coated and even throughout.
Make a well in the center adding buttermilk. Gradually mix into the dry ingredients until fully absorbed. (You may need to bring dough together using your hands toward the end of mixing.)
Turn out onto a lightly floured non-stick surface. Turn a couple of times to bring together and lightly coat with flour.
Press or roll into a circle ¾-1 inch thick. Use a 3 inch cutter and cut into rounds. Re-roll scraps, shape and cut until all dough is used. Place rounds 2 inches apart on pan. Brush tops with melted butter.
Bake for 16-18 minutes or until golden and puffed.
Serve immediately brushed with additional butter, if desired.