Preheat the oven to 350℉ (180℃). Grease a 10-inch (25cm) tube pan, bundt or ring mold with butter and sprinkle with sugar to coat.
To make the cake, cut the mandarins into quarters, peels and all. Remove and discard the stem nubbin and seeds. Puree until smooth in a food processor or blender, then set aside.
In a large bowl, whisk together the oil, sugar, Fiori di Sicilia, and salt. Add the eggs one at a time, whisking as you go; then stir in the pureed mandarins and pistachio flour. In a separate bowl, sift together the all-purpose flour, baking powder, and baking soda and add this slowly to the large bowl, continuing to mix until all the flour is incorporated.
Now scrape the batter into the prepared pan and bake for 45** to 55 minutes (this will depend on the pan you used), or until the cake is nicely browned and fragrant and the top is firm when you touch it lightly.
Cool for 10 minutes, then remove from the pan and transfer to a serving plate. The cake will keep, covered, at cool room temperature for up to a week.