The Cupcakes:
Preheat oven to 350 degrees F. Insert 12 cupcake liners into a 12-muffin tin.
Chop pecans and put them into a small skillet set over medium heat. Cook, stirring frequently, until the nuts are just starting to turn brown. Watch them closely they do not burn. Remove from heat and set aside to cool.
In a medium bowl, whisk together flour, baking soda, salt, ground cinnamon, and ground cloves.
In a large bowl, stir together granulated sugar, unsweetened applesauce, and canola oil until thoroughly combined. Add 2 eggs, one at a time, stirring well after each addition.
Gradually add the flour mixture and stir until just combined. Add grated carrots, golden raisins, pecans, and grated fresh ginger. Stir to combine.
Scoop the batter into the prepared muffin tin, filling each liner about ¾ full. Bake until a toothpick inserted in the middle of the cupcakes comes out clean, about 18 to 22 minutes. Let the cupcakes cool in the pan for 15 minutes, then remove and let cool completely on a wire rack.