Preheat oven to 350 F
Prepare an 8x8 inch or 9x9 inch cake pan by lining it with parchment paper and lightly grease it.
Zest your oranges so that you end up with 1 heaping tablespoon of orange zest and set aside. (While zesting, stop when you see the white part because it is bitter)
Cut up the oranges, and separate out the pulp (remove seeds if any). Puree the pulp and keep it aside along with all its juices (you should end up with about 1 cup).
In a large bowl, sift the dry ingredients--- all purpose flour, salt, baking powder and baking soda. Use a hand whisk to mix them well.
In a stand mixer fitted with a whisk attachment or hand held mixer, add eggs and sugar. Start whisking it on medium speed for about 5 minutes. The mixture should look light and fluffy. Make sure to scrape down the sides of the bowl at least once.
With the mixer still running, SLOWLY DRIZZLE oil.
Then add the orange zest, buttermilk, orange blossom/vanilla essence and pulp puree.
Continue whisking for 1 minute more.
Add the dry ingredients into the wet batter and use a SPATULA to fold it. Keep folding gently until no dry flour can be seen. Do not overmix!
Pour the batter into the prepared tin and give it a few taps on the counter-top to get rid of the air bubbles.
Place into the preheated oven and bake for 35-40 minutes. Check for doneness by inserting a toothpick in the middle. It should be clean with few moist crumbs. It should not be a wet batter.
Place the cake on the cooling rack and allow it to cool completely before adding the glaze.