Heat the oven to 450°F.
In a bowl, mix together the flour, baking powder and soda, salt, shredded mozzarella, smoked salmon, and chives. Place the bowl in the fridge. On the large holes of a box grater, grate the butter into small pieces. Mix into the flour mixture.
Slowly add the buttermilk, mixing in with a rubber spatula or wooden spoon until a soft dough forms. Turn onto a lightly floured surface and fold and pat down until the dough comes together in a circle or rectangle, about 1 ¼ inch thick.
Use a biscuit cutter (2-2.5 inches) and cut out biscuits. Place on a parchment paper lined baking sheet and freeze for 15 minutes. Bake from frozen for 15-18 minutes or until slightly golden. Let cool and enjoy!