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Preheat oven to 425°F (218°C). Spray a 12-count muffin pan with nonstick spray or use greased/sprayed cupcake liners. This recipe yields 14-16 muffins, so prepare a second muffin pan in the same manner or bake in batches and reserve leftover batter at room temperature for when the first batch is done.
Whisk the flour, baking soda, cinnamon, ginger, salt, and flax 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 with a wooden spoon or rubber spatula, then add the raisins and pecans. Fold everything together just until 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 then, keeping the muffins in the oven, reduce the oven temperature to 350°F (177°C). Bake for an additional 18 minutes or until a toothpick inserted in the center comes out clean. The total time these muffins take in the oven is about 23-24 minutes, give or take. (For mini muffins, bake 13-14 total minutes at 350°F (177°C) the whole time.) Allow the muffins to cool for 10 minutes in the pan, then transfer to a wire rack to cool until ready to eat.
Cover leftover muffins and store at room temperature for 2 days or in the refrigerator for 1 week.