Preheat the oven to 375°F (190°C).
Lightly coat a 12-cup muffin tin with cooking spray.
In a medium bowl, whisk together the whole wheat pastry flour, baking soda, cinnamon, nutmeg, ginger, and salt.
In a large bowl, combine the applesauce, Greek yogurt, brown sugar, canola oil, and egg. Stir until smooth and well blended.
Gradually add the dry ingredients to the wet mixture and stir until just combined.
Fold in the shredded carrots, golden raisins, and chopped pecans.
Divide the batter evenly among the prepared muffin cups.
Bake for 7 minutes.
Remove the muffin tin briefly and place one pecan half on top of each muffin.
Return to the oven and continue baking for 7 to 9 minutes, or until a toothpick inserted into the center comes out clean.
Allow the muffins from this Whole Wheat Carrot Muffin Recipe to cool in the pan for a few minutes before transferring them to a wire rack.
Serve warm or at room temperature.