Warm the pot: Heat 1–2 tablespoons of olive oil in a large soup pot over medium heat.
Sauté the aromatics: Add onion, carrots, and celery.
Cook 6–8 minutes, stirring, until softened and lightly golden. Add garlic and cook 30 seconds, just until fragrant.
Build the broth: Pour in the chicken broth. Add Italian seasoning, bay leaf, a pinch of red pepper flakes if using, and the Parmesan rind.
Bring to a gentle boil.
Simmer: Reduce to a lively simmer and cook 10 minutes to meld flavors. Taste and adjust salt and pepper now, before adding pasta.
Add chicken: Stir in the shredded chicken and simmer 2–3 minutes to warm through.
Cook the tortellini: Add tortellini and cook according to package directions, usually 3–5 minutes for fresh. Stir occasionally so they don’t stick.
Finish with greens: Turn heat to low.
Remove the Parmesan rind and bay leaf. Stir in spinach and let it wilt, about 1 minute.
Brighten and garnish: Add lemon juice and chopped parsley. Taste and adjust seasoning.
Serve hot with extra Parmesan if you like.