Preheat oven to 350°F / 175°C. Lightly grease a nonstick hot dog-bun pan.
In a large bowl, whisk together the flour, 1/2 cup / 100g of the sugar, baking powder, and salt until combined. Set aside.
In a separate bowl, stir together the egg yolks, oil, orange juice, orange zest, and vanilla.
Add the dry ingredients to the egg yolk mixture and whisk together until smooth. Set aside.
In a stand mixer fitted with the whisk attachment, combine the egg whites (5 total) and cream of tartar and beat on high speed until medium peaks form, about 2 minutes. Turn the speed to medium-low and slowly sprinkle the remaining 1/4 cup / 50g sugar to create a French meringue. Turn the speed to high and beat until stiff, glossy peaks form, 1 to 2 minutes more.
Stir 1/3 of the meringue mixture into the egg yolk mixture to loosen it up. Then, using the whisk attachment or a rubber spatula, fold the remaining meringue into the yolk mixture.
Fit a 16-inch / 40cm pastry bag with a large round tip (Ateco #9807), pour the batter into the bag, and then pipe into the prepared pan, filling each mold only 2/3 full.
Bake until golden and a tester comes out clean, 15 to 20 minutes. Invert the pan and tap gently to remove the cakes onto a sheet of parchment paper. Let cool completely.