Preheat oven to 325° F. Generously coat a bundt pan with an even layer of olive oil, then sprinkle in a couple tablespoons of sugar. Shake the pan around over the sink until the inside is completely coated with sugar. Set the pan aside.
In a medium bowl, whisk together cake flour, baking powder, baking soda, kosher salt, and cardamom. Set aside.
Place sugar and orange zest in a large bowl or the bowl of a stand mixer fitted with the paddle attachment. Using your fingers, rub together the sugar and zest until evenly incorporated. This activates the essential oils in the zest, adding even more fragrance and citrus flavor. The sugar should be tinted the same color as the zest when you’re finished.
Pour the olive oil into the sugar mixture. Beat on medium speed for 3-5 minutes, or until the sugar has started to dissolve into the oil.
Beat in eggs one at a time until just incorporated, being careful not to over-mix. Finally, beat in orange juice and vanilla extract.
Add about a third of the dry ingredients into the wet ingredients. Mix on medium-low speed until just combined. Add half of the Greek yogurt and beat until just combined. Repeat this process until all the dry ingredients and yogurt have been added.
Scrape down the bowl with a rubber spatula to incorporate any dry ingredients left around the sides. Pour into the greased and sugared bundt pan and smooth the top with the spatula.
Bake in the top half of the oven for 45-50 minutes, or until a cake tester comes out clean. Allow to cool in pan for 15 minutes, then remove cake from pan and transfer to a cooling rack to cool completely.
Once the cake is cooled, make the glaze by mixing the powdered sugar and 2 tablespoons orange juice in a small bowl. Pour the glaze over the cake, then slice and enjoy!
Notes
No cake flour? Make your own with cornstarch and all-purpose flour! Just add 2 tablespoons of cornstarch into a 1-cup measuring cup, then top off the cup with all-purpose flour.
To measure a scant cup of sugar, measure a full cup and then scoop a couple tablespoons off the top.