Prep the chicken. Pat the chicken dry and season with salt, pepper, and half the Italian seasoning.
Smaller pieces cook faster and absorb more flavor.
Cook the tortellini. Bring a large pot of salted water to a gentle boil. Cook tortellini according to package directions until just al dente. Reserve 1/2 cup pasta water, then drain.
Brown the chicken. Heat olive oil in a large skillet over medium-high heat.
Add chicken in an even layer and cook 5–7 minutes, stirring once or twice, until golden and cooked through. Transfer to a plate.
Build the garlic base. Lower heat to medium. Add butter to the skillet.
Stir in garlic and red pepper flakes and cook 30–45 seconds until fragrant. Don’t let the garlic brown.
Make the sauce. Pour in chicken broth and milk. Scrape up any browned bits from the pan.
Simmer 2–3 minutes to warm through.
Thicken with Parmesan. Reduce heat to low and whisk in Parmesan a handful at a time until melted and smooth. If too thick, loosen with a splash of reserved pasta water; if too thin, simmer 1–2 more minutes.
Add greens and chicken. Stir in spinach until just wilted. Return the chicken and any juices to the pan.
Season with remaining Italian seasoning, salt, and pepper. Add lemon juice to brighten.
Combine with tortellini. Gently fold in the cooked tortellini, coating every piece in the sauce. Warm for 1–2 minutes so flavors meld.
Finish and serve. Taste and adjust seasoning.
Top with extra Parmesan and chopped parsley. Serve hot.