Preheat oven to 180°C (350°F). Grease pan with butter, sprinkle on flour and tap out excess.
Zest and juice the oranges, and set aside 150 ml juice* (see notes) with pulp.
In a mixing bowl, cream together orange zest, softened butter, sugar, and yogurt until smooth.
Mix in the eggs, vanilla and orange juice.
In a separate bowl, whisk together flour, baking powder, baking soda and salt. Fold into the wet ingredients until just combined.
Pour the batter into the prepared pan.
Bake for 20 minutes uncovered, then cover loosely with foil and bake another 30–40 minutes, or until a toothpick inserted into the center comes out clean.
Remove from oven and cool in the pan for at least 20 minutes, then transfer to a wire rack or cutting board to cool completely.
Notes
If your oranges don't produce 150ml of juice then you can make up the rest with more fresh orange juice, store-bought orange juice or water.