Preheat your oven to 350°F (175°C). Grease an 8-inch round cake pan and line the bottom with parchment paper.
Place the whole oranges in a pot and cover them with water. Bring to a boil and simmer for about 1 hour until the oranges are soft. Drain and let them cool.
Once cooled, cut the oranges in half and remove any seeds. Place the entire oranges (peel included) into a food processor and blend until smooth.
In a large mixing bowl, whisk together the sugar and eggs until pale and fluffy, about 3-4 minutes.
Stir in the pureed oranges, ground almonds, ground pistachios, baking powder, and salt until well combined.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 40-45 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.
Once cooled, dust the top with powdered sugar if desired before serving.