Begin by preheating your oven to 425°F (218°C). Prepare a 12-count muffin tin by spraying it with nonstick spray or lining it with greased or sprayed cupcake liners. Since this recipe makes 14–16 muffins, have a second muffin pan ready or plan to bake in batches. If you bake in batches, leave the remaining batter at room temperature until the first batch is done.

In a large mixing bowl, whisk together the whole wheat flour, baking soda, ground cinnamon, ground ginger, salt, and ground flaxseed if you're using it. In a separate medium bowl, whisk the eggs until frothy, then add in the brown sugar, honey, oil, applesauce, orange zest, orange juice, and vanilla extract. Whisk these together until everything is well combined. Stir in the shredded carrots and grated apple.

Now, pour the wet mixture into the dry ingredients. Using a wooden spoon or rubber spatula, gently stir the mixture just until all the flour is incorporated. Be careful not to overmix. Fold in the raisins and chopped pecans.

Fill the prepared muffin cups to the brim with the batter. Place the muffins in the preheated oven and bake for 5 minutes at 425°F. Without opening the oven door, lower the temperature to 350°F (177°C) and continue baking for another 18 minutes, or until a toothpick inserted into the center of a muffin comes out clean. The total baking time should be about 23–24 minutes.

Once done, let the muffins cool in the pan for about 10 minutes before transferring them to a wire rack to cool completely. Store any leftover muffins covered at room temperature for up to 2 days, or refrigerate them for up to a week.