2 small or 1 large spaghetti squash (3–3 1/2 pounds), halved lengthwise, seeded
1 1/2 teaspoons (or more) kosher salt, divided
2 tablespoons extra-virgin olive oil
1 pound ground turkey
1/2 teaspoon ground allspice
1/2 teaspoon ground cinnamon
1/4 teaspoon cayenne pepper
3 tablespoons apple cider vinegar
1 onion, finely chopped, divided
2 cups low-sodium chicken broth
1 (14-ounce) can kidney beans, drained, rinsed
1 (14-ounce) can tomato sauce
1 tablespoon unsweetened cocoa powder
1/4 cup chopped parsley
1/4 cup sliced pitted black olives
Preheat oven to 375°F. Season squash with 1 tsp. salt. Arrange face down on a parchment-lined rimmed baking sheet. Bake squash until interior is tender when flipped and prodded with a fork, 20–40 minutes depending on size.
Meanwhile, heat oil in a large, deep-sided skillet over high. Add turkey and cook, breaking up with a wooden spoon and stirring occasionally, until well browned, about 8 minutes. Reduce heat to medium. Add allspice, cinnamon, cayenne, three-quarters of the onion, and 1/2 tsp. salt and cook, stirring occasionally, until tender, 8 minutes. Increase heat to high. Stir in vinegar, scraping up browned bits from bottom of pan. Add broth, beans, tomato sauce, and cocoa powder and stir to combine. Bring to a boil and continue to cook, stirring occasionally, until thickened slightly, about 15 minutes. Season with salt, if needed.
Scrape spaghetti squash out into strands with a fork. Divide among bowls, then spoon chili over. Top with parsley, olives, and remaining chopped onion.