Squeeze the juice from half an orange. Finely grate the clean orange peel using a small grater, making sure to use only the orange part and avoid the bitter white pith.
Place the grated orange zest, orange juice, eggs, and sugar into a bowl. Beat with a hand mixer on high speed for 5–6 minutes, until the mixture becomes pale, creamy, and doubles in volume.
Slowly pour the oil into the mixture in a thin stream, mixing continuously at medium speed until fully incorporated (about 15–20 seconds).
Add the flour, baking powder, and salt to the mixture. Gently fold in using a spatula or mix on low speed just until combined. Transfer the batter into a piping bag (or use a spoon) and fill the muffin cases about ¾ full. Let the batter rest in the fridge for 30 minutes. Meanwhile, preheat the oven to 250°C.
Sprinkle sugar on top of the muffins. Lower the oven temperature to 220°C and bake for about 15 minutes. Let them cool completely, then serve or store in an airtight container.