Combine the first 6 (dry) ingredients in a mixing bowl and stir until completely blended together.
Make a well in the center and add the applesauce and olive oil. Stir together to form a stiff batter.
Work in the chopped walnuts.
With clean, floured hands, form into balls about 1 inch in diameter. Arrange on a parchment-lined baking sheet, and flatten each lightly with your palm.
If you’d like, press a walnut half into each cookie.
Bake for 8 to 10 minutes, or until the bottoms are just starting to turn golden. Don’t overbake, as these crisp up a bit as they cool.
Allow to cool on the baking sheet for a few minutes, then carefully transfer to a plate.