Preheat oven to 350 degrees.
Spray cooking oil on 2 eight inch round cake pans.
Zest 2 blood oranges.
Add zest to 1 cup sugar.
Remove peel, membranes, and pith from 2 oranges. Cut into 1/4" pieces.
Juice the 3rd blood orange for about 1/4 cup of juice.
Add juice to the zest/sugar mixture.
Add the buttermilk or yogurt to this mixture, whisk well.
Whisk in beaten eggs.
Whisk in vanilla extract.
In another bowl, whisk together flour, baking powder, baking soda, and salt.
Whisk dry ingredients into wet ingredients.
Add orange segments, or blend them in with a hand held mixer (which I did in this case, not choosing to use large chunks of oranges).
Fold in olive oil.
Pour batter into pans.
Bake cake for 30 minutes or until golden and a knife inserted into center comes out clean.
Cool cakes in their pans on racks.
Poke holes all over the top of each cake layer.
Keep the cakes in their pans for the pouring of the orange syrup.