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Center the oven rack; preheat the oven to 400°F.
Bring a large pot of salted water to a boil. Add the oranges to the boiling water, cover the pot, and let the oranges boil until perfectly soft -- 60-90 minutes.* Drain, cool, and cut the fruit into quarters. *The longer the fruit boils, the less bitter it will be.
Put the quartered oranges in the bowl of a food processor. Process to a fairly-fine puree.
In a large bowl, whisk the eggs until pale and thick. One ingredient at a time, whisk in the almond flour, salt, sugar, baking powder, and the orange puree.
Pour the batter into the prepared pan, and bake until firm -- about 1 hour. (Hint: check the cake after 45 minutes. If the batter is turning dramatically dark, cover the pan loosely with aluminum foil, then continue baking.) Transfer the pan to a wire rack to cool. Run a plastic knife between pan and cake, then release the cake onto a serving platter or cake stand. Dust with the optional confectioners' sugar.