Heat the oil in a large pot or Dutch oven over medium heat. Add the onion and couscous. Cook, stirring occasionally, until the onion is soft and the couscous is lightly browned, 8 to 10 minutes. Add the garlic and rosemary. Cook, stirring occasionally, until fragrant, 1 to 2 minutes.
Add the broth, chicken, ½ teaspoon salt, and ¼ teaspoon pepper and bring to a boil. Reduce heat and simmer, stirring occasionally, until the chicken is cooked through and the couscous is tender, 15 to 20 minutes. Remove the chicken and, using 2 forks, coarsely shred; return it to the pot. Stir in the spinach.
Serve topped with the Parmesan.
Yummy! And easy to make.