Preheat oven to 200°C/180°C fan-forced. Line a 12-hole, 1/3 cup-capacity muffin pan with paper cases.
Sift flours and spice into a bowl. Stir in sugar and carrot. Whisk honey, eggs, buttermilk and oil together in a jug. Add honey mixture to flour. Mix until just combined (do not over-mix).
Spoon mixture into muffin holes until three-quarters full. Bake for 25 minutes or until a skewer inserted in the centre of 1 muffin comes out clean. Cool in pan for 2 minutes. Turn out onto a wire rack to cool completely.