Preheat the oven to 425 degrees F (220 degrees C).
In a medium bowl, stir together the flour, baking powder, sugar, salt and cream of tartar. Cut in butter using a fork until it looks crumbly. Make a dip in the center of the dry mixture and add the milk, cheese and parsley into the bowl. Mix until a soft dough forms.
Roll or pat out on a floured surface to 3/4 inch thick. Cut into circles and place on a baking sheet.
Bake for 10 minutes in the preheated oven, or until the bottoms of the biscuits are golden brown.