Preheat oven to 350 degrees and position baking rack in the center of the oven. Spray a 9-inch springform pan with nonstick cooking spray and line the bottom of the pan with a piece of parchment paper; set aside.
In a blender, combine the pieces of orange, sugar, oil, eggs, and vanilla. Place the lid on the blender and blend until the mixture is well combined and the oranges are puréed.
To the blender, add in the flour, baking powder, and salt. Place the lid on and pulse until the mixture is well incorporated, stopping to scrape down the sides of the blender with a rubber spatula as needed.
Pour the cake batter into the prepared baking pan. Place on center rack in oven and bake for 40-45 minutes, or until a toothpick inserted in the center of the cake comes out clean. Place on baking rack to cool for 10 minutes, then carefully remove the collar from the pan and cool completely.
Dust the top of the cooled cake with powdered sugar, cut into slices and serve.
