Start 15-20 charcoal briquettes in a chimney starter. When charcoal is lit, pour into a campfire ring, or other prepared area.
Mix flaxseed meal with water and set aside.
Spready charcoal briquettes and place Dutch oven directly over hot coals.
Add oil and sauté onion, bell pepper, carrots, and celery until softened. Add garlic and sauté for 1-minute.
Stir in spices and toast until they become fragrant.
Start an additional 15-20 charcoal briquettes in the chimney starter.
Stir in zucchini, beans, tomatoes, tomato paste, and vegetable broth. Simmer uncovered for 15-20 minutes, stirring occasionally.
While chili simmers, mix together corn muffin mix, flaxseed meal "egg", and soy milk.
Spoon cornbread batter on top of chili.
Cover Dutch oven. Place 8-10 coals under the Dutch oven, and 15-18 coals on top of the lid.
Bake for 25-30 minutes, rotating the lid and Dutch oven 90° every 10 minutes for even heat.
Check doneness with a toothpick or knife - cornbread should be golden and set.