Cut shortening and very cold butter into dry ingredients of flour, salt and sugar.
Slowly pour milk into your dry ingredients. Mix lightly. Fold in grated Parmesan cheese and chives.
Pour dough onto a lightly floured surface and gently pat into a round disc about ½ inch thick. Cut dough with a sharp metal or glass cutter.
Add about 2 tablespoons of shortening to your baking pan and place into oven to melt, about 2 or 3 minutes. Once melted, remove from oven and tilt pan to make sure the bottom of the baking pan is well-coated.
Carefully place each biscuit into the hot grease on the baking pan. You’ll hear a bit of a sizzle as the bottom of the biscuit fries a bit in the hot grease.
Brush tops with buttermilk and then sprinkle with additional chives.
Place the baking pan into the oven and bake until the biscuits have risen and are lightly browned, about 10 – 12 minutes. Remove from oven and serve warm.