HEAT OVEN TO 350F/177C. Spray 9 inch (23cm) springform pan with oil. Note 1 for other pan options.
PREPARE ORANGES: Using a sharp knife, place orange on cutting board and slice off the thin top orange layer all around the orange. Try to get as little of the white pith layer as possible (leaving on some is fine - no need to obsess!). Then slice off the white pith layer and discard. Repeat with second orange. Cut oranges into quarters. Shortcut: If your oranges only have a very thin layer of pith, you can use the whole orange.
CREAM BUTTER, SUGAR, EGGS: Place butter, sugar and eggs in food processor bowl. Process for 2 minutes until fluffy and creamy. Scrape down sides of bowl once or twice. Scoop mixture into medium-large bowl.
GRIND ORANGES: Place oranges and orange peels in food processor. No need to clean out processor first. Process until finely blended, about 1 minute. Scrape orange mixture into bowl with butter mixture.
FINISH BATTER: Add baking powder and flour. Gently fold into wet mixture just until incorporated. Do NOT over mix or the cake will be dense. Pour batter into prepared pan. Tap pan on counter to level the batter evenly.
BAKE: for 45-50 minutes or until cake no longer jiggles when shaken and when cake tester or toothpick is inserted in center and comes out clean. Two 8" round pans will take less time, about 25-35 minutes. Timing depends on size of oranges (amount of liquid in cake) and your oven (all ovens are different and not perfectly accurate on temperatures). Remove from oven and let cool for 10 minutes before removing on pan. Cool completely on cooling rack before frosting.
MAKE FROSTING/GLAZE (OPTIONAL): While cake is baking, whisk icing/confectioner sugar, 1/2 of orange juice and orange zest with a fork. Add more orange juice until you get the consistency you like. Note 3 for traditional orange buttercream frosting.
DECORATE: Sprinkle orange cake with powdered icing sugar (through a sieve) if not using frosting. If using frosting/glaze, spread it on top of cake letting it slip down the sides if desired. Decorate cake with orange zest strips, orange slices, drained mandarin oranges, zest or crushed nuts if you like.