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Place the chickpeas in a pan and cover by 2 inches (5cm) with water. Add ½ teaspoon baking soda, stir, and bring the water to a boil. Remove the pan from the heat, cover, and let sit for 1 hour. Drain the chickpeas and cover them with fresh water. Bring to a boil over medium-high heat, reduce the heat so the water is boiling gently and cook until the chickpeas are nearly tender through, about 1 hour.
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Heat the oil in a large, heavy kettle or saucepan over medium heat. When the oil is hot but not smoking, add the meat and brown it well on all sides, which will take about 9 minutes. Add the onions, stir so they are coated with oil, and cook until they are deep golden, about 10 minutes, then crumble the saffron over the mixture. Season it with the salt, stir, and 1 cup (250ml) of the hot water. Stir and cook for 4 to 5 minutes, to blend the ingredients and allow the saffron to soften. Add the tomato paste and the 2 quarts (2 liters) of hot water, bring to a boil, cover, and reduce the heat so the liquid is simmering merrily. Cook until the meat begins to turn tender, about 30 minutes.
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Add the carrots and the chickpeas, bring to a boil covered, reduce the heat so the liquid is boiling gently and cook until the carrots resist slightly when tested with a sharp knife, about 15 minutes. Add all the remaining vegetables and cook until they are tender, about 30 minutes. Check the seasoning and remove from the heat. The soup is ready to serve, but will benefit from sitting for an hour or two and being reheated.