Wash oranges well. Place oranges inside a large pot and cover with water. Bring water to a boil, lower heat to simmer, and cover. Simmer for 2 hours, turning oranges occasionally if they're floating above the water line.
Grease a 9 inch springform pan with butter and preheat the oven to 350F.
When oranges are cooked, transfer them to a cutting board, reserving orange water. Let cool until they're okay to touch, then cut into large pieces and remove any seeds you see.
Transfer oranges to a food processor and puree until smooth. If mixture is really dry, add a bit of orange water to loosen, although it's unlikely you'll need much. Set aside.
Using an electric mixer, beat together eggs and sugar until they are light and fluffy, about 5 minutes. Add in vegetable oil and beat for 30 seconds. Add in orange puree and beat on low until combined.
In a large bowl, combine baking powder, almonds, flour, and salt. Pour dry ingredients into mixer bowl and stir until combined.
Pour the batter into your greased springform and bake for 45-75 minutes, until a cake tester comes out mostly clean from the center of the cake. Let cake cool completely.
Use a knife to run along the edges of the springform, then remove the sides and transfer cake to a cake stand or plate. Dust with powdered sugar before serving.