Coat the bottom of a large pot with 2 tablespoons of olive oil and place it over medium heat. When the oil is hot, add the mushrooms. Cook about 4 minutes on each side, until lightly browned. Remove the mushrooms from the pot and transfer to a plate.
Add the remaining 2 tablespoons of oil to the pot. Once the oil is hot, add the onion and bell pepper. Sauté for about 5 minutes, until the pepper is soft and the onions translucent. Add the garlic and cook about 1 minute more, until very fragrant.
Return the mushrooms to the pot and stir in the wine. Raise the heat and bring it to a simmer. Lower the heat and allow to simmer, uncovered, for about 5 minutes, until reduced by about half.
Stir in the chickpeas, diced tomatoes, fire roasted tomatoes, crushed tomatoes, broth, sugar, red pepper flakes, and bay leaves. Bring the mixture to a simmer and allow to cook for about 15 minutes, stirring occasionally, until the sauce thickens up a bit and the mushrooms are very tender. Stir in the zucchini and continue cooking for about 5 minutes more, until tender.
Remove from heat and remove the bay leaves. Season the stew with salt and pepper to taste, and adjust any other seasonings to your liking.
Ladle into bowls and top with fresh parsley and basil. Serve with bread.