Heat oven to 400 degrees F. Place squash in a large rimmed baking pan and toss with 1 tablespoon of the oil and 1/4 teaspoon of the salt. Bake at 400 degrees F. for 30 minutes. Set aside.
In a large pot, heat remaining tablespoon oil over medium-high heat. Add onions, peppers and garlic. Cook 8 minutes, stirring occasionally. Add tomatoes, chili powder, cinnamon, sugar, allspice and remaining 1/2 teaspoon salt. Simmer 15 minutes over medium-low heat, with lid ajar. Stir occasionally.
Stir in cooked squash and beans. Simmer 5 minutes.
Serve chili over cooked spaghetti. Scatter cheese, oyster crackers and scallions over the top.