Preheat the oven to 400 degrees F. Grate the rind of about 1/2 the orange, about 1 teaspoon. Squeeze half the orange to get 2 tablespoons of juice. Set the juice aside

Mix the teaspoon of rind into the sugar with your fingertips, squeezing the two ingredients together into the sugar is uniformly orange. Set aside about one tablespoon of the orange sugar for topping - the rest goes into the biscuits. 

Whisk the flour, baking powder, cream of tartar, and salt together in a medium sized bowl. Add the major portion of the orange sugar and whisk again until the sugar is well dispersed. 

Add the shortening, either by hand (using a pastry cutter or two knives) or with a few short bursts in a food processor. 

Add the buttermilk and 2 tablespoons of orange juice to the flour and shortening mixture, either with a fork or again, short bursts in a food processor. In either case, mix only until the dough comes together. On a well-floured counter or mat, pat out the dough into a 6-7-inch circle about 3/4-inch high. 

Cut the biscuits out with a 2- 2 1/2-inch biscuit cutter, cookie cutter, or cup. 

Brush the top of the biscuits with the tablespoon of buttermilk or melted butter, then sprinkle on the reserved orange sugar. 

Place the biscuits on an ungreased cookie sheet and bake for 15-20 minutes, until the biscuits are golden. Cool on a wire rack.