Preheat oven to 350 degrees F (175 degrees C). Grease an 8x8-inch baking dish.
Combine acorn squash, 1/3 cup brown sugar, 1/4 cup flour, egg, milk, vanilla extract, 1 teaspoon cinnamon, nutmeg, and cloves in a food processor. Pulse to mix. Transfer squash mixture to a bowl and stir in chopped apples, carrot, and raisins. Spread filling into prepared baking dish.
Mix rolled oats, wheat bran, 1/4 cup brown sugar, whole wheat flour, and 1 teaspoon cinnamon in a small bowl. Drizzle with melted butter and toss to combine. Sprinkle crumble mixture over filling.
Bake in preheated oven until filling is bubbly and topping is browned, 30 to 40 minutes.