Preheat oven to 350. Spray a 9? springform pan, tube pan or cake pan with cooking spray (I used a tube pan).
Grind walnuts in food processor until finely ground, but not powdery. Add flour, baking powder, baking soda and salt and pulse briefly to combine.
In mixer, beat eggs until frothy, 2 minutes or so. Add sugar and honey, and continue to beat until thick and pale, 3-4 minutes. Lower speed and add walnut / flour mixture in steps until just mixed. Add orange juice, applesauce, orange zest and olive oil and beat just until combined.
Pour batter into prepared pan. Place pan on baking sheet lined with foil and bake until tester comes out clean, approximately 40 minutes.
Cool cake completely on rack. If desired, dust with powdered sugar before serving.