Preheat the oven to 350°F. Spray a 9x5" loaf pan with nonstick cooking spray.
In a small bowl, combine flour, baking soda, baking powder, salt, and spices.
In a medium bowl, whisk the oil, eggs, brown sugar, granulated sugar, applesauce and vanilla until incorporated. Then stir in the finely grated carrots.
Add the dry ingredients and mix until just combined. Use a spatula to fold in the walnuts and raisins.
Pour batter into the prepared pan and top with the crumble topping. Use your fingers to press the topping together to create big chunks!
Bake for 45-55 minutes, or until a toothpick inserted in the center comes out clean, with a few moist crumbs. If cake is browning too much during baking, tent it with a piece of foil.
Allow the bread to cool in the pan for 10 minutes before transferring to a cooling rack.