Line a 9" circular cake pan with parchment paper (I use a pencil to trace an outline of the bottom of the pan on the paper, then cut slightly inside the line) and grease generously with olive oil, under and over the parchment paper and up the sides of the pan. Preheat your oven to 325 degrees F and place an oven rack in the top third of the oven.
In a large bowl, whisk together the olive oil (3/4 cup), orange zest (1 teaspoon), orange juice (1/4 cup), honey (3/4 cup), three eggs, Greek yogurt (1 cup), ground cardamom (1/2 teaspoon), ground cinnamon (1/2 teaspoon), kosher salt (1/4 teaspoon), baking powder (1/2 teaspoon), and baking soda (1/2 teaspoon).
Add the flour (1 1/2 cups) and whisk until well-combined.
Pour into prepared cake pan. Bake at 325 degrees F in the top third of the oven for 45-60 minutes, or until toothpick inserted in center of the cake comes out clean (see notes).
Allow to cool in pan on cooling rack for at least 10 minutes. Run knife along the edge to loosen and flip onto a cutting board to remove, then flip back over onto the serving dish.
Dust with confectioners' sugar through a sifter or by placing it in a mesh sieve and tapping it.
Slice into 8 pieces. Serve warm or at room temperature, drizzled with honey and sprinkled with extra orange zest, if desired.
This cake is dense and very moist. Some readers have noted that theirs did not cook all the way in the middle. This recipe may have varied results if you are at a higher elevation, if you use a different size cake pan, if your yogurt is particularly watery or lower in fat, your oven temp, or even depending on brand of flour. If yours seems like it's not cooking in the middle after 70 minutes or so, I recommend tenting with foil, so the top of the cake doesn't burn, and turning the temperature of your oven up to 350 degrees F until it's cooked.
This cake can be stored at room temperature in an airtight container for about three days. For best results, dust with confectioners' sugar just before serving. Otherwise, it will disintegrate into the moisture of the cake.
Leftovers can be frozen and stored in an airtight bag or wrapped tightly in plastic for up to 3 months.
The provided nutrition information does not include any added sodium from seasoning to taste, any optional ingredients, and it does not take brands into account. Feel free to calculate it yourself using this calculator or by adding the recipe to Yummly.