Preheat oven to 400° F.
Stir together flour, sugar, baking powder, salt and baking soda.
Cut the butter into chunk and add to the flour mixture with the cheese and basil. Add the buttermilk, mixing lightly with a fork until combined.
On a floured board, knead the dough gently 20 times. Roll out the dough to a 1/2-inch thickness. With a 2" circle cookie cutter, cut the dough and place on a greased cookie sheet.
Bake at 400° F for 10 minutes. Reduce the temperrature to 325° F and bake 10 minutes longer, or until golden brown.