Put chickpeas and kidney beans in separate bowls, and cover with plastic wrap; let soak overnight at room temperature.
Drain and rinse. Transfer chickpeas and kidney beans to separate medium saucepans. Cover with water by 1.5 inches. Bring to a boil. Reduce heat; simmer until tender about 50 minutes for kidney beans and 1 hour for chickpeas. Drain.
Heat oil in a 6-quart stockpot over medium-high heat until hot but not smoking. Add onion, carrots, celery and garlic. Cook, stirring occasionally, until onion is translucent, about 6 minutes. Add mushrooms, bell pepper, and chile. Cook until pepper and chile are just tender, about 8 minutes. Stir in tomato paste, spices, oregano, 2 teaspoons salt, the pepper Worcestershire, and wine. Add crushed tomatoes, 3.5 cups water, chickpeas, kidneybeans, and bulghur.
Bring to a simmer. Reduce heat; gently simmer until thick, about 30 minutes. Season with satl. Serve with cheese, cilantro, and sour cream.
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