Combine milk and sugar in a small bowl, whisk to combine. Place the biscuit mix in a medium bow. Cut the cold butter into the mix with a pastry blender until you have coarse crumbs. Add the grated cheese to the bowl, toss to combine. Add the milk mixture, stir gently until you have a soft sticky dough. Drop the dough by rounded Tablespoons onto the parchment paper, keeping the dough about 2 inches apart on the baking sheet.