In a large bowl, whisk the eggs with sugar until dissolved. Add orange zest and juice, then whisk in while adding the oil.
Sift in the flour with the baking powder; add the half amount to the mixture, mix until smooth. Add the remaining half amount of flour with salt, whisking until fully combined.
Pour the batter into cupcake molds, filling each about ¾ full.
Bake for 20 to 25 minutes or until golden and a toothpick comes out clean.