As chickpeas dry, start preparing the soup: In a Dutch oven or heavy stockpot, combine soaked chickpeas, 5 cups water, 1 tablespoon olive oil, bay leaves and ½ teaspoon salt over high heat. Bring to a boil for 2 to 3 minutes, then reduce heat to a simmer, cover and cook until chickpeas are tender, about 1 to 2 hours.
Heat oven to 400 degrees. While chickpeas are cooking, cut bread into thick slices, then tear slices into bite-size pieces. Place bread in one layer on large rimmed baking sheet and toast until crisp and light brown, about 10 minutes. Let cool on pan and set aside.
Finish the crunchy chickpeas: Raise oven temperature to 425 degrees. Remove the towels from baking sheet with the chickpeas, and toss the chickpeas with 2 teaspoons olive oil, ½ teaspoon salt and za’atar until well coated. Roast until golden and crispy, about 13 to 18 minutes, tossing halfway through. When chickpeas are still hot, sprinkle lightly more salt. Taste and add more salt or za’atar, or both, if you’d like.
When the chickpeas for the soup are tender, discard bay leaves. Using a slotted spoon, transfer 2 cups of chickpeas, ½ cup of chickpea cooking liquid and ¼ cup olive oil to a blender or food processor, and purée until smooth.
In a large skillet over medium-high, heat the remaining 2 tablespoons oil until shimmering. Add the onion and cook, stirring occasionally, until softened, about 5 minutes. Add garlic and cook until golden, about 2 minutes. Add the remaining 1 teaspoon salt, 1 tablespoon cumin and tomato paste and cook, stirring, until fragrant, 1 minute. Add a splash of the chickpea cooking liquid to the pan, and bring to a simmer to deglaze, scraping up the browned bits on the bottom of the pan. Turn off heat.
