Preheat oven to 425F. Line your muffin tray with cupcake liners.
Mill your flour so that you have 2 cups worth.
Whisk the flour, baking soda, cinnamon, salt, and flaxmeal in a large bowl. In a medium bowl, whisk the eggs, honey, oil, applesauce, and vanilla together until combined.
Whisk in the carrots and apples.
Pour the wet ingredients into the dry ingredients, and stir slowly with a wooden spoon or spatula. Add the raisins. Fold everything together just until combined.
Spoon batter into the liners, filling them all the way to the top.
Bake for 5 minutes; then, keeping the muffins in the oven, reduce the oven temperature to 350F. Bake for 15-18 minutes or until a toothpick inserted in the center comes out clean.
Allow the muffins to cool in pan for 10 minutes, then transfer to a wire rack to cool until ready to eat.
Cover leftover muffins and store at room temperature for up to 2 days.