Whisk together flour, salt, baking powder and baking soda. Cut the butter into the flour using a pastry cutter, fork or even by hand until mixture resembles wet sand. Stir in the grated cheese and chives. Then slowly add as much sourdough starter as needed until a soft dough forms.
Turn out dough onto a floured surface and knead a couple of times.
Flatten the dough slightly and cut into 10-12 biscuits using a biscuit cutter. Place biscuits on a baking sheet lined with parchment paper. Bake for 12-15 minutes or until golden brown.