Preheat oven to 400 degrees F. Spray a muffin tin (either a 12 hole regular size or a 6 hole large size) with non-stick cooking spray.
In a large bowl, whisk together flour, sugars, baking powder, baking soda, cinnamon, salt and ginger until well blended.
Zest both oranges into flour mixture and mix well.
After zesting, peel oranges (and seed, if necessary) and place in a blender with the orange juice. Blend oranges and juice on high for 30 seconds, or until oranges are pureed. Add egg and butter and blend on high again for 10 seconds.
Add orange mixture to flour mixture and stir until dry ingredients are just moistened.
Fill muffin cups 1/2 full. Bake for 18 - 22 minutes for regular muffins, 21 -26 minutes for large muffins, or until a toothpick inserted comes out clean.
Let cool for 5 minutes and remove from tin to a rack. If desired, drizzle with orange glaze. Combine 1 cup powdered sugar with enough orange juice to create a glaze that will drizzle over the muffins.