Heat the oven to 400 degrees.

Sift the flour, baking powder, baking soda and salt together into a medium bowl.

Add the shortening and work it into the flour mixture with a pastry cutter. Cut the cold butter into the flour mixture with a pastry cutter or fork until all the butter has been added.

Slowly add the buttermilk and mix together until the mixture begins to form a ball.

Transfer the dough to a lightly floured surface and pat it into a large disc 1/2 to 3/4 inch thick.

Cut out biscuits with a 3 inch round cutter or the top of a glass. Reroll any leftover dough to form additional biscuits.

Arrange biscuits on an ungreased baking sheet and brush with melted butter. Bake for about 18 minutes, until the tops are golden brown. Serve warm.