Preheat your oven to 175°C (350°F). Grease a 9-inch round cake pan with a little olive oil and line the bottom with parchment paper. This will help prevent sticking and make removing the finished cake easier.
Wash the oranges thoroughly and dry them. Finely grate the orange zest, taking care not to include the bitter white pith. Squeeze the oranges to obtain fresh juice and remove any seeds. Freshly squeezed juice gives the cake a brighter citrus flavor.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, cardamom, nutmeg, and salt. Mixing these ingredients first helps distribute the raising agents and spices evenly throughout the batter.
In a separate large bowl, whisk the eggs and granulated sugar until the mixture becomes slightly pale and well combined. This step helps create a lighter texture and ensures the sugar is evenly incorporated.
Gradually pour the olive oil into the egg mixture while whisking continuously. Continue mixing until the ingredients form a smooth, slightly thick mixture. Use a mild, fruity olive oil if you prefer a delicate flavor, or a more robust extra-virgin olive oil for a pronounced Mediterranean character.
Stir in the fresh orange juice, orange zest, and vanilla extract. Mix until evenly combined. The citrus aroma should be noticeable, with the vanilla adding a gentle sweetness.
Add the dry ingredients to the wet mixture in two or three batches. Fold gently with a spatula or whisk until no large streaks of flour remain. Avoid overmixing, as excessive mixing can make the cake dense.
Pour the batter into the prepared cake pan and gently smooth the top. Tap the pan lightly on the counter to release any large air bubbles. If desired, sprinkle a small pinch of cinnamon over the surface for extra fragrance.
Bake for 40–50 minutes, or until the cake is golden and a toothpick inserted into the center comes out clean or with a few moist crumbs. If the surface browns too quickly, loosely cover the cake with aluminum foil during the final part of baking.
Remove the cake from the oven and let it cool in the pan for 10–15 minutes. Carefully transfer it to a wire rack and allow it to cool further before glazing or slicing. This helps the cake set properly and prevents it from breaking.
If you want a glazed finish, whisk the powdered sugar with 1 tablespoon of orange juice and the orange zest. Add a little more juice if necessary until the glaze reaches a thick but pourable consistency.
Drizzle the glaze over the completely cooled cake. Alternatively, dust it with powdered sugar and garnish with thin orange slices or chopped pistachios. Slice and serve with tea, coffee, or a spoonful of Greek yogurt.