Unsalted butter, for pan
2/3 cup cake flour (not self-rising), plus more for pans
2 large whole eggs plus 1 large egg yolk
1/2 teaspoon coarse salt
1/2 teaspoon baking powder
Confectioners' sugar, for dusting
Preheat oven to 325 degrees. Butter four 1-cup mini Bundt pans; dust with flour, tapping out excess. Whisk whole eggs, yolk, and sugar until foamy. Add oil in a slow, steady stream, whisking constantly until combined.
Whisk together flour, salt, and baking powder in a small bowl. Fold flour mixture into egg mixture in 3 batches.
Divide batter evenly among prepared pans; smooth tops with an offset spatula. Bake until light golden and a cake tester comes out clean, about 20 minutes. Transfer pans to a wire rack to cool 10 minutes. Turn out cakes, and serve warm, dusted with confectioners' sugar.