Preheat the oven to 350°F. Spray muffin cups with nonstick spray or line them with paper liners.
In a large bowl, stir together the flours, sugar, cinnamon, baking soda, and salt. Add the carrots, pecans, raisins, and coconut and toss to combine well.
In a medium bowl, whisk together the oil, eggs, buttermilk, and vanilla. Add to the carrot mixture with the grated apple and stir just until the batter is combined. Don’t worry about getting all the lumps out – overmixing will make the muffins tough.
Fill the prepared muffin tins almost to the top. Bake in the middle of the oven for 25-30 minutes, until the muffins are golden and the tops are springy to the touch.
Tip them in their cups to help them cool by allowing steam to escape.