Preheat the oven to 425 degrees F.
Into a bowl, sift together the flour, baking powder, baking soda, and salt and blend in the shortening until the mixture resembles meal.
Add the buttermilk, stir the mixture until it just forms a dough, and gather it into a ball. On a lightly floured surface knead the dough gently 6 times and pat it out into a rectangle, roughly 1/2-inch thick.
Using a knife, divide the dough into 12 even-sized squares. Separate the squares and invert the squares onto a lightly greased baking sheet.
Brush the tops of the squares with the milk, bake the biscuits in the middle of the oven for 12 to 15 minutes, or until they are pale golden, and transfer them on to a rack. Serve the biscuits at room temperature.