Nonstick olive oil spray
1-1/2 Cups chopped walnuts
1 Cup all purpose flour
1 Tbsp baking powder
Preheat oven to 350F. Spray a 9-in diameter springform pan with nonstick olive oil spray. Place a round of parchment in the bottom of the pan, and also spray the paper with the nonstick spray.
Pulverize the walnuts in a food processor until the nuts are fairly finely ground — but not so ground up as to be powdery. Combine ground walnuts, flour, and baking powder in a medium mixing bowl; set aside.
Using a mixer with its whisk attachment, beat the four eggs in large mixing bowl until they become frothy (about 2 min). Gradually pour in the sugar, whisking until the sugar-egg mixture is light, thick, and pale yellow (about 4 min). Add the walnut-flour mixture, a little at a time; then add the orange juice, orange extract, and olive oil, continuing to beat until mixture is just blended.
Transfer cake batter to the prepared springform pan. Place the pan on a rimmed baking sheet, and bake the cake until a toothpick inserted into the center of the cake comes out clean, about 60 min.
Cool cake completely in pan on rack, 1 hour or more. Release springform pan sides. Gently invert the cooled cake onto a cake plate or platter, and gingerly remove the parchment paper from what was previously the bottom of the cake. Sprinkle powdered sugar atop cake and serve.