Preheat oven to 190°C. Grease a 15 hole muffin tin with first measure of oil, or line with cases.
In a medium bowl, mix flour, bran, baking soda and cinnamon.
In a large bowl, beat together oil, honey and eggs until smooth. Mix in vanilla, yoghurt, milk and apple.
Gradually add dry mixture to wet mixture until combined. Spoon mixture into muffin tin, careful not to overfill. Bake muffins for about 20 minutes, or until an inserted skewer comes out clean. Allow to sit for 10 minutes before removing from tin. Allow to cool completely. Store in an airtight container for up to 5 days, or freeze.