Make the cake: Preheat the oven to 350°F (180°C). Grease an 8-inch square cake pan with olive oil and line with parchment paper.
2. Step
In a medium bowl, whisk together the flour, baking powder, baking soda, and ½ teaspoon salt.
3. Step
Add the sugar and citrus peels to a food processor. Pulse for about 1 minute, until the peels have mostly broken down into fine pieces. Reserve 1 tablespoon of the citrus sugar in a small bowl. Transfer the remaining citrus sugar to a large bowl.
4. Step
Add the olive oil and 1 cup of coconut milk to the citrus sugar in the large bowl. Whisk until thoroughly combined.
5. Step
Add the flour mixture to the sugar mixture. Whisk just until no dry spots remain; do not overmix.
6. Step
Pour the batter into the prepared baking dish, using a silicone spatula to scrape all of the batter from the bowl.
7. Step
Bake the cake for 55–60 minutes, until the edges are golden brown and a toothpick inserted into the center comes out clean.
8. Step
Let the cake cool in the pan for 20 minutes, then carefully invert the cake onto a wire rack. Peel off the parchment, then carefully flip right-side up. Let cool completely, about 2 hours.
9. Step
Make the icing: In a medium bowl, whisk together the powdered sugar, 2 tablespoons coconut milk, and the salt until smooth. The icing should be thick, but pourable. Add the remaining tablespoon of coconut milk if needed.
10. Step
Pour icing over the center of the cake, then use an offset spatula to push toward the edges. Let set for 1–2 minutes, then sprinkle the reserved citrus sugar over the top. Let the icing harden for at least 30 minutes, up to 2 hours before slicing.
11. Step
Slice into 9 squares. Store leftovers in a lidded container at room temperature, up to 2 days.
12. Step
Garnish with candied citrus peels if you like. Enjoy!
