Place a can’s worth of chickpeas on a clean kitchen towel or a double layer of paper towels, and pat them dry.

In a large soup pot, heat 1 tablespoon olive oil over medium-high. Add the chickpeas and ½ teaspoon salt, and cook, stirring occasionally, until crisped, 6 to 10 minutes.

Add another tablespoon of oil, sliced garlic, cumin seeds and crushed red pepper to the pot (save the grated garlic for later). Cook until the garlic is golden brown at the edges, 2 to 3 minutes. Use a slotted spoon to transfer the chickpeas and garlic to a plate. While the crispy chickpeas are still hot, sprinkle them with more salt to taste.

Add the remaining 2 tablespoons oil to the pot and heat until it thins out, about 30 seconds. Add onion, ground cumin and a pinch of salt, and cook until very soft and brown at the edges, 5 to 7 minutes.

Add 3 cups broth, remaining chickpeas and ½ teaspoon salt, and bring to a simmer. Simmer until the soup is nice and flavorful, adding more salt to taste if needed, 10 to 15 minutes.

Stir in the tahini, cilantro and grated garlic. Using an immersion or regular blender or a food processor, purée the soup, making it smooth or leaving it chunky, as desired, then add it back to pot if necessary. If it seems too thick, thin it down with some or all of the remaining broth.

Squeeze some juice from the lemon halves into the pot, adding as much as you like to make the soup lively and bright. Ladle the soup into bowls and serve topped with the crispy chickpeas and a drizzle of olive oil or more tahini, and a sprinkling of paprika if you like, with pita chips on the side.