Heat the oil or vegan butter in a large Dutch oven over medium-high heat.
Add the chopped onion, celery, and carrots and sauté for 5–7 minutes, until the onion is golden and vegetables are softened.
Stir in the minced garlic and Italian seasoning and cook for about 30 seconds until fragrant.
Sprinkle the all-purpose flour over the vegetables and cook, stirring, for about 1 minute to remove the raw flour taste.
Add the drained chickpeas and the broth, stirring well to dissolve the flour into the liquid.
Increase the heat to high, cover, and bring the soup to a boil.
Uncover, add the dry orzo, stir, reduce heat to medium, and simmer for about 10 minutes or until the orzo is tender, stirring frequently to prevent sticking.
While the soup simmers, make the gremolata by combining the finely chopped parsley, lemon zest, and a pinch of salt in a small bowl; set aside.
When the orzo is cooked, reduce heat to low and stir in the baby spinach and lemon juice (start with juice of 1/2 lemon and add more to taste). Season with salt and black pepper to taste.
Ladle the soup into bowls and garnish each serving with the parsley gremolata and an optional drizzle of olive oil.
