Preheat the oven to 350°F (180°C). Butter and flour a 9-inch cake pan.
Make the buttermilk, mixing the milk with orange juice and lemon juice. Set aside.
In a bowl, rub the sugar with the orange zest with your hands until you get a moist and fragrant sugar.
Add the eggs and beat with the sugar with a hand whisk. Beat vigorously for a minute until the eggs are light and foamy.
Add the olive oil and continue mixing until combined.
Sift the flour with the baking powder and mix half into the batter.
Add the buttermilk and continue mixing.
Finally, add the rest of the dry ingredients and mix until combined. Finish mixing with a spatula to reach the edges and bottom of the bowl.
Pour the batter onto the buttered pan and cover the entire surface with sugar before baking.
Bake in a preheated oven at 350°F (180°C) for 45 to 50 minutes. The cake will be ready when poking with a knife, it comes out clean. Wait 10 minutes and unmold. Wait for it to cool before serving.
For the glaze, beat the icing sugar with the orange juice with a handheld or stand mixer with a paddle attachment until pale and smooth.
Drizzle each slice with glaze and supremed peeled orange wedges. You can also cover the whole cake with the orange glaze.