In a large mixing bowl combine the flour, baking powder and baking soda. Give the ingredients a quick whisk to mix them together. Add the butter to the dry ingredients and use a pastry cutter (or your hands) to incorporate the butter into the flour until it resembles small crumbly pieces.
Use a wooden spoon to stir in the beaten eggs, mixing until combined. Add the buttermilk to the mixture, mixing with the spoon until combined. The dough will be thick and very sticky. Cover the bowl with plastic wrap and place in the refrigerator to chill for at least 30 minutes (if your baking them now) or chill them over night (if your baking them tomorrow).
Preheat the oven to 400 degrees. Line a baking sheet with parchment paper. Set aside.
Scrape the dough onto a well floured work surface. Flour your hands as well. Use your hands to press the dough into a round that is roughly 14 inches across and 1/2 inch thick. Use a floured 2 and 3/4 inch biscuit cutter to cut out about 20 biscuits. You may need to collect and pat out more dough from the scraps.
Arrange the biscuits on the prepared baking sheet, arranging them that they are all touching.
In a small bowl combine 1 egg and the extra table spoon of buttermilk and beat the ingredients together. Lightly brush the mixture over the top of each biscuit.
Bake for 15-20 minutes, or until golden brown. Allow to cool for 5 minutes and then serve immediately.