Preheat oven to 400 degrees and set oven rack to the middle position. Line a baking sheet with parchment paper, set aside.
In a medium-sized bowl, gently toss flour, brown sugar, baking powder, baking soda and salt.
In a separate small bowl, whisk sour cream and egg until completely smooth. Set aside.
Grate frozen butter into mixture. Using your hands, work in the butter until the mixture resembles a coarse meal. Add both cheeses, reserving 2 tablespoons for later, chives and ham. Gently stir in sour cream mixture until just about combined. Do not over work the dough! Again, very gently press the dough against the sides of the bowl a few times and form a ball. The dough will be sticky at first but will come together as you form it.
Place dough on a lightly floured surface and lightly pat into an 8" circle about 3/4" thick. Use a very sharp knife to cut into 8 triangles (like a pizza). Transfer triangles onto prepared baking sheet. You can arrange them in two rows, 4 in each row, or arrange them in a circle shape - leaving about 1" between each one. Sprinkle reserved cheese on top of scones.
Bake scones for 15-17 minutes or until the tops begin to golden. Don't take them out too early or they will be too soft. Allow them to cool for 10 minutes on the pan before transferring onto a wire rack to finish cooling completely.