Make sure to rinse your quinoa well in cold water before using.
In a small pot, bring broth, dill sprig, lemon peel, and garlic to a boil. Season with salt. Reduce heat and simmer, covered, 10 minutes. Uncover; remove dill sprig and lemon peel. Increase heat to medium-high and add quinoa; cook, stirring occasionally, until tender, 8 to 10 minutes. Remove from heat. Stir in spinach, chopped dill, and lemon juice. Drizzle with oil, season with pepper, and serve.