Bring a large pot of salted water to a boil. Wash the oranges and place them in the boiling water; cover pot. Boil until very soft, about 1 hour. Drain, cool, cut into quarters, removing any seeds. You can do this the day before, refrigerating oranges after cooling.
Preheat oven to 325°F Grease and line the bottom of a 9" springform pan with parchment paper
Place chopped oranges in a food processor fitted with a steel blade. Process on high, scraping down the sides, until it's pureed with only a few visible bits of rind remaining; it does not need to be completely smooth. Add orange sugar, pulsing until combined.
Add in eggs, almond extract; pulse. Add almond flour and baking powder. Pulse until combined and batter is blended.
Pour into prepared pan. Bake 60 minutes, checking after 45 minutes to tent surface with foil to prevent overbrowning. Bake until the surface is golden and a toothpick inserted into the center comes out clean.
Cool fully in cake pan.
If desired add cream-glaze to cake when cooled. Make a double recipe if you’re wanting extra to serve on the side. Alternatively, dust with confectioners' sugar instead of glaze. Garnish with additional orange slices or orange peel if desired.
Cake is very moist so it’s best to refrigerate whether you use add the cream cheese glaze or not. Flavor improves as it ages and it good chilled, served from the fridge. Enjoy up to 5 days for best flavor.