Place a colander in the sink. Fill a large bowl with ice water.

Trim spinach stems and discard. Wash spinach leaves thoroughly. Heat a wide pot over medium-low heat. Add spinach to pot, along with any water clinging to leaves, and toss until wilted. Drain in colander, then quickly plunge into ice water. When cooled, quickly drain again and squeeze dry. Transfer to a food processor, along with garlic, onion, lemon juice, and salt. Pulse until spinach is finely chopped.

Spoon yogurt into a medium serving bowl; whisk until smooth. Add spinach mixture, then gently stir in buttermilk and dill, followed by chickpeas. Soup may be served immediately or chilled for a few hours. Stir before serving.