Heat olive oil in a Dutch oven over medium.
Peel all garlic cloves; set two garlic cloves aside. Thinly slice remaining garlic cloves.
Add onion, sliced garlic, salt, black pepper, and red pepper.
Cook, stirring often, until garlic just starts to turn golden, about 10 minutes.
Add wine to pan, stirring to loosen any browned bits. Add tomatoes, crushing with your hands (or buy crushed tomatoes).
Stir in chicken stock, rosemary, basil, Parmesan rind, lemon zest and juice, and chicken.
Simmer 10 minutes, stirring occasionally. Remove rosemary and basil sprigs, and Parmesan rind.
Stir in frozen tortellini, spinach, and grated Parmesan.
Grate 2 remaining garlic cloves using a Microplane; stir into soup. Simmer 5 minutes more.
Garnish servings with additional basil and grated Parmesan.