Place a rack in the center of your oven and preheat it to 325ºF. Generously coat a 9-inch round baking dish with nonstick spray. Line the bottom with parchment paper and spray once more.
In a large mixing bowl, briskly whisk together the sugar and the eggs until they are pale and foamy, about 1 minute.
Whisk in the yogurt, olive oil, vanilla, espresso powder, cinnamon, and salt until smoothly combined.
Whisk in the cocoa powder until smoothly combined. Sprinkle the baking powder and baking soda over the top, then sprinkle on the flour. Whisk until everything is evenly incorporated (stop stirring shortly after the dry ingredients disappear. There may be some small lumps which is fine).
Fold in the chocolate chips.
Pour the batter into the prepared pan and with a spatula or the back of a spoon, smooth the top. Rap the pan on the counter a few times to remove any air bubbles.
Bake the chocolate olive oil cake until the edges are beginning to pull away from the edges, the center is puffed, and a toothpick inserted in the center comes out clean, about 30 minutes. Place the pan on a wire rack to cool for 15 minutes, then gently unmold and let cool completely on the rack. Transfer to a serving plate. Dust generously with powdered sugar, slice, and serve.
Notes
*If using regular cocoa powder, use an additional 1/4 teaspoon baking soda (3/4 teaspoons total) to balance out the acidity.
TO STORE: Store the cake wrapped (or in an airtight container) at room temperature for up to 3 days. You can refrigerate it for up to a week.
TO FREEZE: Wrap the cake well, first in a layer of plastic and then in a layer of foil. Freeze for up to 3 months and thaw in the refrigerator before serving. You will likely need to dust it with powdered sugar again.