Freeze butter in advance.
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.
Use a box grater to shred frozen butter. (medium grate) Use a fork to stir the butter shreds into the flour mixture until evenly distributed.
To the bowl add ham, cheddar cheese and chives. Stir until coated with flour and evenly distributed.
Make a well in the center of the flour mixture, adding buttermilk. Use a rubber spatula to gradually mix the buttermilk into the dry ingredients until fully absorbed. (You may need to bring the dough together using your hands toward the end of mixing.)
Turn out onto a lightly floured nonstick surface. Turn a couple of times to bring together and lightly coat with flour, just until it's no longer sticky.
Press or roll the biscuit dough into a circle 3/4-1 inch thick. Using a 2.5-inch or 3-inch biscuit cutter to cut the dough into rounds. Repeat, rolling any scraps together, pressing the dough and cutting into rounds, until all of the dough has been used.
Place biscuit dough 2-inches apart on the prepared pan. Brush the tops with melted butter.
Place pan into the oven. Bake for 16-18 minutes or until golden brown and puffy.
Serve immediately brushed with additional butter, if desired.