1: Preheat oven to 350°F. Spray a 9-inch-diameter springform pan with nonstick olive oil spray and place parchment paper round in bottom of pan.
2: Grind walnuts in processor until finely ground but not powdery. Combine ground walnuts, flour, and baking powder in a medium bowl and set aside.
3: Ensure the eggs are at room temperature. Using an electric mixer, beat eggs in a large bowl until frothy, about 2 minutes.
4: Gradually add sugar, beating until light, thick, and pale yellow, about 4 minutes.
5: Gradually add walnut-flour mixture, then add orange juice, orange zest, and olive oil, beating just until blended.
6: Transfer batter to prepared pan and place the pan on a rimmed baking sheet.
7: Bake cake until a tester inserted into the center comes out clean, about 1 hour.
8: Cool the cake completely in the pan on a rack, then brush with leftover syrup from the candied oranges.
9: Arrange the candied orange slices on top.
