Preheat the oven to 350°F (180 C). Brush a standard loaf pan with olive oil or spray it with baking spray.
In a large mixing bowl, combine the sugar and orange zest. Use your fingers to rub the zest into the sugar until the sugar is a light orange color and the zest is evenly distributed throughout. Add the Greek yogurt, olive oil, eggs, and orange juice and whisk to combine.
Add the flour, baking powder, baking soda, and salt. Stir gently with the whisk just until combined and no streaks of dry flour remain.
Pour the batter into the prepared pan and smooth the top. Bake for 50 to 55 minutes, or until a toothpick inserted in the center of the cake comes out clean.
Let the cake cool in the pan for 10 minutes. Then, tip the cake out of the pan and onto a wire rack to finish cooling to room temperature.
While the cake is cooling, make the glaze. Whisk together the powdered sugar and orange juice in a small bowl until smooth. The glaze should be thick but pourable. If it’s too thick, add more orange juice, 1 teaspoon at a time, to reach the desired consistency.
Pour the glaze over the top of the cake, allowing it to run down the sides. Let it set completely before slicing and serving. Top with dark chocolate shavings.
