Preheat oven to 400°F.
Place flour, baking powder, salt, and baking soda in a large bowl.
Add slices of cold butter and using a pastry cutter, cut the butter into flour mixture until it resembles coarse sand.
Make a well in the center and add buttermilk. Stir mixture together until a shaggy dough starts to form.
Place dough onto a lightly floured work surface and pat dough into a rectangular shape about ½ inch thick. You can use a rolling pin for this.
Sprinkle ½ the shredded cheese and green onions onto the surface of the dough.
Using a dough scraper, fold the dough into thirds.
Roll out to ½ inch thickness, using a rolling pin.
Sprinkle the remaining cheese and green onions onto the dough. Reserve some of the cheese to sprinkle on top of the biscuits.
Using a dough scraper, fold the dough into thirds and roll out the dough into ½ inch thick square shape with a rolling pin.
Cut out 9 square biscuits with the dough scraper.
Place biscuits on a cookie sheet and baste with buttermilk. Sprinkle each biscuit with about a teaspoon of the remaining shredded cheese.
Bake biscuits until light golden brown and cheese is bubbly and melted, about 20 minutes.
Transfer biscuits to a wire rack to cool.
