Step 1

In a large saucepan over medium-high, melt 2 tablespoons butter. Add the onion, carrots and ½ teaspoon salt; cook, stirring occasionally, until the vegetables are lightly browned, 4 to 6 minutes. Add 1 teaspoon cumin seeds, ¼ teaspoon cayenne and ¼ teaspoon black pepper; cook, stirring, until fragrant, about 2 minutes. Add the chickpeas and the 1 cup reserved liquid, the garlic, 4 cups water and ¼ teaspoon salt. Bring to a boil over medium-high, then reduce to medium-low, cover and cook, stirring occasionally, until the garlic is soft when the head is squeezed with tongs, 30 to 35 minutes.

Step 2

Remove the pot from the heat. Squeeze the garlic cloves from the head into the chickpea mixture; discard the empty skins. Let the chickpea mixture cool for about 5 minutes.

Step 3

Meanwhile, in a small saucepan over medium-high, melt the remaining 3 tablespoons butter. Add the remaining 2 teaspoons cumin seeds and cook, stirring, until fragrant and the butter has stopped foaming, 1 to 1½ minutes. Add the sesame seeds and another ¼ teaspoon cayenne (if using); cook, stirring, until the sesame seeds are toasted and fragrant, about 1½ minutes. Remove from the heat and set aside, covered.

Step 4

Using a blender and working in batches so the jar is never more than half full, puree the chickpea mixture until smooth. Return the soup to the pan and cook over medium-low, stirring often, until warmed through, 2 to 5 minutes. (Alternatively, use an immersion blender to puree the soup directly in the saucepan.) Taste and season with salt and black pepper. Serve drizzled with the butter mixture.