1. Mince garlic. peel carrots and slice 1/4 inch thick. Chop onion fine and mince celery. Mince 2 teaspoons thyme.
2. Heat oil and garlic in Dutch oven over medium low heat, stirring occasionally, until garlic is light golden, about three minutes. Add carrots, onion, celery; increase heat to medium; and cook, stirring occasionally, until vegetables are softened, 5 to 7 minutes.
3. Stir in thyme and cook until fragrant, about 30 seconds . Stir in broth, scraping up any browned bits, bring to simmer.
4. While broth comes up to a simmer, mince 2 tablespoons parsley. Trim chicken, cut into 3/4 inch pieces, and season with salt and pepper.
5. Stir orzo into broth, return to simmer, cover, and cook over medium low heat, adjusting heat as needed to maintain simmer, about 6 minutes, until orzo is just tender. Stir chicken into soup and cook until chicken is cooked through and orzo is tender, 3 to 5 minutes.
6. Stir in spinach and cook until spinach is wilted, 1 to 2 minutes. Off heat, stir in parsley and season with salt and pepper.