Preheat the oven to 350°F (175°C). Grease and line a 9x5-inch loaf pan.
In a large bowl, whisk together the flour, baking powder, and salt.
In a separate bowl, rub the zest into the sugar to release the citrus oils. Add the yogurt, oil, eggs, orange juice, and vanilla, and mix until smooth.
Gradually fold the wet ingredients into the dry ingredients until just combined.
Pour the batter into the prepared pan and bake for 45-55 minutes, or until a toothpick comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
Notes
Store in an airtight container at room temperature up to 3 days.