Preheat oven to 325o degrees and adjust oven rack to middle position. Butter and flour a 10-cup bundt pan.
In a medium bowl, whisk the flour, baking soda, salt, and baking powder until incorporated. Set aside.
In a food processor fitted with the blade attachment (a smoothie blender will also work), pulse the prepared chunks of oranges until only small flecks of the rind remain - the mixture should be smooth but not fully pureed.
In the mixing bowl of a stand mixer fitted with the paddle attachment, (or large mixing bowl for hand-held mixer), cream the butter and sugar on medium speed until light and fluffy - about 3-5 minutes. Add in one egg at a time and beat until incorporated after each. Add the vanilla extract with the last egg.
Spoon in 1 and 1/2 cups of the orange mixture to the batter and mix until incorporated. The remaining orange mixture will be used for the glaze.
Turn the stand mixer on low and slowly add in 1/3 of the flour mixture to the batter. Mix until just incorporated. Next add 1/2 of the buttermilk, again mixing until incorporated. Repeat adding 1/3 of the flour, then buttermilk, ending with the remaining flour.
Scrape the batter into the prepared bundt pan and smooth out the top with a spatula.
Bake until the cake has risen and is firm to the touch, and when a skewer (or a knife) inserted into the center of the cake comes out with only a few crumbs clinging - about 55-60 minutes.
Let the cake cool in the pan on a wire rack for 10 minutes. Invert the cake onto the wire rack and cool completely.