Bring a large pot of water to boil to cook the tortellini. Place the stock in another pot and bring it to simmer. Add the tortellini to the boiling water and cook until tender. Meanwhile, add the chicken and kale to the stock and simmer 5 to 6 minutes, or until the chicken is cooked through. Stir in the pesto, taste the soup, and season with salt and black pepper, if needed. Reserve on medium-low heat until the tortellini is tender.
When the tortellini is cooked, drained well and divide among 4 large soups bowls. Ladle the chicken/kale mixture overtop and serve. If desired, at the table, top the soup with pinches of crushed chili flakes and freshly grated Parmesan cheese.