Heat a large Dutch oven or heavy-bottomed pot over medium heat. Add the butter, diced onions, carrots, celery, and mushrooms. Sprinkle with a small pinch of salt to help the vegetables release their moisture. Sauté for 8–10 minutes, stirring occasionally, until the butter has melted and the vegetables begin to soften.
Stir in the minced garlic and frozen ginger. Cook for another 1–2 minutes, stirring frequently, until fragrant. Keep everything moving so the garlic doesn't burn.
Pour in the chicken bone broth and add the Italian seasoning, allspice, and bay leaves. Stir everything together and bring the soup to a gentle simmer. Let it simmer for 10–15 minutes to give the vegetables time to soften and the flavors time to develop.
For even more flavor, you can add a parmesan rind while the soup simmers, then remove it before serving.
While the soup simmers, bring a separate pot of water to a boil. Cook the cheese tortellini according to the package directions, then drain.
Stir the cooked shredded chicken and tortellini into the soup. Let everything warm through for a few minutes. If you're adding baby spinach or fresh spinach, stir it in now and cook just until wilted.
Remove the bay leaves, taste the broth, and add salt and black pepper as needed. You can also add a pinch of red pepper flakes if you like a little heat.
Ladle the chicken soup with tortellini into big bowls and finish with fresh parsley or parmesan cheese, if desired. Serve warm with crusty bread, garlic bread, crackers, or your favorite soup toppings. Cozy up and enjoy!