Line a baking sheet with a piece of parchment paper.
In a large bowl, combine the cake flour and regular flour, baking soda, baking powder, sea salt, chives and cheddar, and mix all ingredients well.
Add frozen grated butter; just mix lightly so butter is dusted with flour.
Make a well in the center of the bowl and pour in the buttermilk. With a good strong wooden spoon, work the flour into the buttermilk, just until the dough comes together (the dough should just be starting to form - do not over work it).
Dust the counter with a little extra flour, turn the dough onto the flour and shape it into a ¾ inch thick rectangle.
Cut the dough with a circle cutter into the desired size (lightly dust the cutter with flour to help the dough from sticking).
Brush off any extra flour and place the biscuits onto the lined baking sheet. Brush the tops with a little buttermilk to help them colour.
Bake at 425°F for 15 - 20 minutes. Rotate tray for even cooking after first 8 minutes and continue to bake until golden brown.