Preheat oven to 350ºF (180ºC). Grease an 8x8" baking dish or line with parchment paper.
Beat butter and sugar on medium speed of electric mixer until light and fluffy, about 2 minutes. Add egg yolks, one at a time, beating well after each. With mixer on low speed, add the zest and juice from all three oranges. The mixture will appear curdled at first - that's ok. Increase mixer speed to medium and beat until it comes together, pausing to scrape down sides of bowl as needed.
In a separate bowl, whisk flour and baking powder. With mixer speed on low, gradually beat into the butter mixture until just incorporated.
In another bowl, whip egg whites until stiff peaks form. Fold 1/3 of the whites into the cake batter to lighten it up, then gently fold in the rest. (Use a light hand so you don't deflate the whites.) Scrape batter into prepared baking pan and bake for 35-45 minutes, until top feels springy when gently pressed and tester inserted in centre comes out clean or with just a few moist crumbs.