In a large cast iron pot over medium heat, heat the olive oil.
Sauté the onion, garlic, and red and yellow bell peppers until they have cooked down a bit, about 5 minutes.
Add the diced squash, and sauté for another 10 to 15 minutes.
Once the squash is approaching fork-tenderness, add the tomatoes. Give it a good stir, and add the chili powder, red pepper flakes, cumin, paprika, coriander, mustard, allspice, and oregano.
Add 1 cup of broth to the pot, raise the heat to medium-high, and bring the chili to a low boil.
Reduce the heat to simmer, and cook for at least 2 hours.
Stir in the remaining 1 cup of broth in increments when the chili starts getting thick.