Heat the olive oil or vegan butter in a large Dutch oven over medium-high heat until shimmering.
Add the chopped onion, finely chopped celery, and chopped carrots and sauté for 5 to 7 minutes, until the onions are golden and vegetables have 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 imitation chicken or vegetable broth, stirring well to dissolve the flour into the liquid.
Cover and bring the soup to a boil over high heat.
Uncover, add the dry orzo, stir, then reduce heat to medium and simmer for about 10 minutes, stirring frequently, until the orzo is tender and not sticking to the bottom.
While the soup simmers, combine the finely chopped parsley, lemon zest, and a pinch of salt in a small bowl to make the gremolata; 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 additional salt and black pepper as needed.
Ladle the soup into bowls and garnish each serving with the parsley gremolata and an optional drizzle of olive oil.