Preheat oven to 450 degrees F. In a mixing bowl, sift flour, baking powder, baking soda and salt. Blend well. Using a pastry cutter, cut in shortening and butter until it resembles coarse cornmeal. Using a large cooking spoon, blend buttermilk into flour mixture until moistened. On a lightly-floured surface, knead dough until it comes together. Do not overwork dough as the less it is handled, the flakier the biscuits. Break dough into 8 equal portions and pat approximately 1/2-inch thick onto a baking sheet. Biscuits should be irregular in shape, but no more than 1/2-inch high and 1-inch apart. Bake 10-15 minutes or until golden brown. Remove from oven and brush with melted butter. NOTE: To make the famous "Ugly Biscuit," cut dough into 5-inch round and 1/4-inch thick then turn one-third of dough over in a turnover fashion before baking. You may wish to fill turnover portion with ham, bacon and cheese, etc.