Preheat oven to 325℉, placing oven rack in the center. Generously butter a 10-cup Bundt pan.
In the bowl of a stand mixer or using a handheld mixer over a large bowl, cream the butter and sugar until fully, about 3 minutes. Add the eggs, one at a time, beating until just incorporated after each addition.
1 cup butter, 1 ¼ cup granulated sugar, 3 large eggs
In a medium bowl, add the flour, baking powder, baking soda, and sea salt. Set aside.
2½ cups all-purpose flour, 2 tsp baking powder, ¼ tsp baking soda, ¼ tsp sea salt
Trim the ends of the oranges; do not peel them. Cut into large chunks and remove seeds. In a food processor, pulse the orange chunks until the pulp is mostly smooth, don't over process it into a puree. Spoon out 1½ cups of the orange mixture and add this to your batter, beating until blended. Add the flour mixture in two additions and beat until smooth, about 20 seconds. Don't over beat the batter. Smooth the batter into the Bundt pan and smooth the top.
2 oranges
Place the Bundt pan directly on the center rack and bake until the cake has risen and is evenly golden and firm to the touch, 40-50 minutes. A toothpick stuck in the middle should come out mostly clean, but the firm touch of the cake is your best indication that it's done. Remove the cake to cool on a cooling rack set over a baking sheet. Let the cake cool in the pan for 10 minutes then invert it onto the rack and let cool completely.