Heat the olive oil in a large pot set over medium heat. Toss in the onion, celery, and carrots and cook, stirring occasionally, until softened but not browned, 7 to 10 minutes. Add the garlic, paprika, cumin, basil, rosemary, and red pepper flakes and cook, stirring often, until fragrant, 1 to 2 minutes.
Add 1 can of drained chickpeas, the tomatoes with their juices, 4 cups of the broth, and sugar. Bring to a boil, then reduce the heat to medium-low and simmer, uncovered and stirring occasionally, until the liquid has reduced slightly, about 20 minutes. Stir in 1 to 1 1/2 teaspoons salt and pepper to taste. Remove from the heat and let cool slightly.
Purée the soup until smooth using an immersion blender or let the soup cool for 10 minutes and then carefully blend it in batches in a standard blender. Return the soup to the pot, return to low heat, and if a thinner consistency is desired, stir in a little more broth. Stir in the remaining can of chickpeas and the spinach and cook until the spinach wilts, 3 to 5 minutes. Taste and season with more salt, if desired. Pour into bowls and top with a dollop of yogurt or labneh, if desired. Serve hot.