Preheat an oven to 425°F. Line a baking sheet with parchment paper and set aside.
In a large mixing bowl, place the flour inside and quickly add the cold butter. Using a pastry blender or your fingers, cut and mix the flour and butter together until small, coarse crumbs form. Gently stir in the cheese and chives.
Make a well in the middle of the flour and cheddar cheese mixture and pour in the buttermilk and, using a rubber spatula, gently stir together until just incorporated. Do not over mix. Your dough will be very wet and sticky.
Scoop out the biscuit dough using spoons or a cookie scoop, and place onto your lined baking sheet, placing them 1 to 2 inches apart. Brush the tops of the biscuits with the melted butter and sprinkle on a little fresh diced chives if desired.
Bake, rotating the pan from front to back halfway through baking, until the biscuits are golden brown, for about 20 minutes. Let cool for about 10 minutes before serving. Enjoy!