Preheat oven to 350 degrees F. Grease an 8 inch round cake pan. You can line the bottom with parchment paper too if you are worried it will stick.
In a large bowl, add the flour, arrowroot, baking powder, baking soda, and salt. Whisk until well combined.
In a medium bowl, add the olive oil, yogurt, orange zest, orange juice, sugar, and vanilla. Whisk until well combined.
Add the wet to the dry. Use a spatula and mix until just combined. Careful not to overmix.
Pour batter into greased pan. Bake for 30 minutes, or until a toothpick comes out clean. Allow cake to cool in the pan for 20 minutes. Run a knife along the edge and flip cake onto a plate to remove from the pan. Then flip again onto the cooling rack to cool completely.
Once cake is cooled, make the glaze by adding the powdered sugar and orange juice to a small bowl. Whisk until well combined and a thick glaze forms. It may seem like it’s not coming together, but keep stirring and it will slowly turn into a smooth glaze. Add more orange juice for a thinner glaze and more powdered sugar for a thicker glaze.
Pour glaze on top of the cooled cake. Top with extra orange zest if desired. Slice and enjoy! Store leftovers in an airtight container on the counter up to 3 days. It tastes even more flavorful and moist the next day. I would highly recommend making this cake the day before serving, wrapping it in plastic wrap overnight (without the glaze on top). Although it still tastes amazing day of!