In a large bowl, whisk together the flour, baking powder, and baking soda. Add butter, and use a pastry blender to cut the butter into the flour until the pieces are even and about pea-size.

Stir in the beaten eggs until well combined.

Stir in 1 1/2 cups of buttermilk - the dough should now be sticky. If it is too dry, then add more buttermilk a tablespoon at a time, and mix after each addition.

Cover bowl, and refrigerate anywhere from 30 minutes to overnight.

Preheat oven to 400 degrees.

Line baking sheet with parchment paper.

Flour your work surface and place dough on the work surface.

Use your hands and press the dough in a circle, about 1/2" thick.

Use a floured round biscuit cutter to cut out biscuits.

Place biscuits on the parchment-covered baking sheet so they are touching.

Now beat together the remaining egg and 1 TBL of buttermilk and brush this mixture on top of the biscuits.

Bake for 15-20 minutes until slightly golden brown.