Preheat oven to 425°F (218°C). Spray a 12-count muffin pan with nonstick spray or use greased/sprayed cupcake liners.

Whisk the flour, baking soda, cinnamon, ginger, salt, and flaxseed together in a large bowl. In a medium bowl, whisk the eggs, brown sugar, honey, oil, applesauce, orange zest, orange juice, and vanilla together until combined. Whisk in the carrots and apples. Pour these wet ingredients into the dry ingredients, stir a few times, then add the raisins and pecans. Fold everything together until just combined and no pockets of flour remain.

Spoon the batter into liners, filling them all the way to the top. Bake for 5 minutes at 425°F; then, keeping the muffins in the oven, reduce the temperature to 350°F (177°C). Bake for an additional 18 minutes or until a toothpick inserted in the center comes out clean. Allow muffins to cool for 10 minutes in the pan, then transfer to a wire rack.

Cover leftover muffins and store at room temperature for 2 days or in the refrigerator for up to 1 week.