Follow the directions on the package of your barley.
While your barley cooks, peel and grate the carrots. In a large bowl, whisk together honey, juice of one lime, and olive oil. Add the grated carrots and then season with salt and pepper. Stir until the grated carrots are coated. Let the carrots marinate for at least 10 minutes, stirring occasionally.
To a small blender or food processor, add cilantro, lime juice, water, olive oil, salt, and pepper. Blend until the cilantro is in little pieces and it's mixed through.
Once the barley is cooked, add to the pot the spinach, carrots (including the liquid), and cilantro sauce. Stir until combined and season with additional salt and pepper to taste.