Heat the oil in a dutch oven over medium-high heat. Add the carrots, celery, onion, ½ tsp salt, and ¼ tsp pepper. Cook, stirring occasionally, until vegetables are softened, about 6 minutes.
Stir in the garlic and cook until fragrant, about 10 seconds. Pour in the vegetable broth and bring to a boil.
Stir in the orzo and chopped spinach. Reduce heat to medium and simmer until orzo is tender, 8 to 10 minutes.
Take off the heat and stir in the lemon juice and fresh parsley. Season with salt & pepper to taste.
