Preheat the oven to 350°F. Grease a 9-inch round cake pan and line the bottom with parchment paper.
In a large bowl, rub the orange zest into the sugar with your fingertips until fragrant and slightly damp.
Add the orange juice, yogurt, olive oil and vanilla and whisk until smooth and fully blended.
In a separate bowl, whisk together the flour, baking powder, baking soda and salt. Add to the wet mixture, fold gently just until combined and pour into the prepared pan.
Bake for 35-40 minutes, until golden on top and a toothpick inserted in the center comes out clean.
While the cake bakes, simmer the orange juice and sugar for the syrup for 2 minutes until the sugar dissolves. Poke holes all over the warm cake with a skewer and brush the syrup over the top.Cool in the pan for 15 minutes, then transfer to a wire rack and cool completely.
Whisk the powdered sugar, orange juice and orange zest until smooth and thick. Drizzle the glaze over the cooled cake and let it set for 15 minutes before slicing.