Preheat the oven to Gas Mark 7 (425F degrees). Place a large baking sheet (no liner) on the lower oven shelf to heat up.
In a large bowl, whisk together the two flours, baking powder, bicarb, sugar and salt.
In a jug, stir together the milk and vinegar, then set aside (adding an acid such as vinegar, or lemon juice to milk creates a homemade buttermilk substitute).
If you haven't already, grate the frozen butter. Using a pastry blade or table knife, cut the cold grated butter into the dry ingredients until the mixture resembles coarse breadcrumbs. Stir in the grated cheese and finely snipped chives.
Make a well in the centre of the bowl, and add the milk/vinegar mixture. Using the table knife again, combine together until a dough forms (if it seems too dry, add a splash more milk, a little at a time).
Flour your hands and work surface, and tip the dough out on to it. Knead very lightly (only until the ball of dough comes together - for best results try not to handle the dough any more than necessary) then gently press into a round, 3cm (1 inch) deep.
Using an 8cm (3-inch) smooth edged cutter, cut out rounds by sharply pushing the cutter straight into the dough without twisting (this will help the scones to rise more evenly). Repeat, reworking the dough when necessary until you have all eight scones cut out.
Remove the hot baking sheet from the oven (don't forget oven gloves!) and place the scones, evenly spaced, on to it. Brush the scones (tops only, not sides) with the egg wash or milk, and bake for 15-18 mins or until golden brown, well risen and cooked all the way through (cover with foil if the tops are browning too quickly).
Transfer to a wire rack to cool. Scones are best eaten fresh on the day, warm from the oven, with lots of butter. Otherwise, freeze on the day of making and use within one month (place defrosted scones in a warm oven for a few minutes to refresh them).