Preheat oven to 350°F. Grease a 9×13-inch pan and line with parchment, leaving overhang.
Whisk flour, both sugars, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg in a large bowl.
Fold in shredded carrots, walnuts, and raisins to coat with the dry mixture.
Stir applesauce, oil, and vanilla together in a separate bowl until smooth.
Pour wet ingredients into dry. Mix just until no dry streaks remain; do not overmix.
Spread batter evenly in the prepared pan and smooth the top.
Bake 23–27 minutes, until a toothpick in the center comes out mostly clean.
Cool in the pan for 15 minutes. Lift out, cool completely, then slice into bars.