Preheat the oven to 350°F. Prepare the cake pan by lining the bottom with a round piece of parchment paper and lightly greasing the sides.
In a mixing bowl, combine flour, baking powder, baking soda, and salt. Set aside.
In the bowl of a stand mixer, add the sugar and orange zest and use your fingers to massage together until it becomes moist. Add eggs to the sugar mixture and beat together on medium-high speed until light and fluffy.
Lower the speed to medium-low, then add oil, yogurt, and orange juice to the foamy egg mixture. Mix until well combined.
Add the dry mixture to the wet mixture and mix on low speed until just combined. Avoid overmixing.
Transfer to the prepared cake pan. Bake for 35 minutes or until a toothpick inserted into the center comes out clean. Remove from the oven and allow the cake to cool in the pan for about 20 minutes.
While the cake is cooling, whisk together orange juice, powdered sugar, and vanilla for the glaze until smooth.
Transfer the cake to a wire rack, peeling off the parchment paper. Place the rack on top of a parchment-lined baking sheet.
Slowly pour orange glaze over the warm cake. If needed, use the back of a spoon to spread the glaze.