In a large bowl, combine the flour, brown sugar, baking soda, cinnamon, nutmeg and ginger. Combine the eggs, applesauce and vanilla; stir into dry ingredients just until moistened. Fold in the carrots and raisins (batter will be thick).
Spread evenly in a 13x9-in. baking pan coated with cooking spray. Bake at 350° for 30-35 minutes or until a toothpick inserted in the center comes out clean. Cool on a wire rack.