Preheat oven to 450 degrees F. Line a large baking sheet with parchment paper or a silicone baking mat.
In a large mixing bowl, mix the flour, baking soda, baking powder, sugar, and salt until well combined. Cut in the cold butter until the mixture is crumbly - you can use a pastry cutter, food processor, mixer, or fork to do this.
Once the mixture is crumbly, pour the cold buttermilk into the mixture and gently mix (don't over-do!) until it all comes together.
Gently stir in the feta cheese until it's completely mixed in.
Dump the dough onto a lightly floured surface and work it together with your hands. Pat into a rectangle and then fold into thirds (as if you are folding a letter). Turn the dough, gather crumbs, and repeat this procedure 2-3 times.
Place the dough on a lightly floured surface and pat it into a rectangle that's 1/2 inch thick. Use a biscuit cutter (2.5 inch) or a canning jar (wide mouth) to cut the biscuits. Don't twist the glass or biscuit cutter - cut, and then pull straight up.
Gather any scraps and re-pat out to 1.5 inch thickness. Then continue to cut until you work through the remaining dough.
Arrange evenly spaced on your baking sheet, and brush the top with a tiny bit of melted butter.
Bake 15-17 minutes or until golden brown. Remove from oven and allow to cool before enjoying.