Cream butter, shortening (or lard), peanut butter, and both sugars together in a mixing bowl.
Add eggs and beat until combined. Beat in the vanilla, followed by the soda and salt – make sure there are no lumps of stray soda.
Stir in the cake flour, then stir in the all-purpose flour, followed by the chopped nuts.
Chill the dough for about an hour.
Preheat oven to 350 degrees F. Line a couple of cookie sheets with parchment or just use nonstick sheets and don't lined them with anything.
Using a medium size cookie scoop, scoop out about 32 balls of dough and arrange 2 1/2 inches apart on baking sheets. You can leave them as balls or you can use a fork and make a criss-cross pattern.
Bake for 12 - 15 minutes or until lightly browned around the edges. The centers may seem a bit underdone at this point, but they will firm up. Let cookies cool on the pan 5 minutes before transferring to a wire rack to cool completely.