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While the tofu marinates, coat the bottom of a large pot with 1 tablespoon of oil and place over medium heat. Add onion and sauté until very soft and translucent, 10 minutes. Add bell pepper and garlic. Sauté 5 minutes more, until pepper is soft. Remove from pot and transfer to a large plate or bowl.
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Add another tablespoon of oil to the pot, and once hot, add zucchini. Sauté until lightly browned and softened just a bit, about 5 minutes. Transfer to plate or bowl with onion mixture.
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Add remaining 2 tablespoons of oil to the pot, and once hot, add eggplant. Saute until lightly browned and softened, about 10 minutes.
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Return onion and zucchini mixture to the pot. Add tomatoes, water or broth, thyme and bay leaves. Bring the mixture to a simmer, lower heat, and allow to simmer, uncovered, until veggies reach desired tenderness. I let them go for about 30 minutes, so they were very soft, but you can adjust this to your liking. Anywhere between 15 minutes and 1 hour should do. Remove from heat. Discard bay leaves, then stir in basil, and season with salt and pepper to taste.