Bring chicken broth and quinoa to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until most of the broth is absorbed, 10 to 15 minutes.
Stir tomatoes, spinach, and pesto into the quinoa. Simmer until remaining chicken broth is absorbed and quinoa is tender, about 5 minutes. Sprinkle Parmesan cheese over quinoa mixture.