Melt the butter with the olive oil in a large stock pot or Dutch oven over medium heat.
Add the carrots, celery, and leeks. Season with salt and pepper and cook, stirring occasionally, for 8–10 minutes, until the vegetables are softened and the leeks are wilted.
Add the thyme, poultry seasoning, crushed red pepper flakes, and garlic. Cook for 1 minute, stirring, until fragrant.
Sprinkle in the flour and cook for 2 minutes, stirring occasionally.
Slowly whisk in the chicken stock until smooth, then stir in the water.
Increase the heat to high and bring the soup to a boil. Once boiling, reduce the heat to medium and add the tortellini.
Simmer for 8–10 minutes, stirring occasionally, until the tortellini are almost al dente.
Stir in the cooked chicken, heavy cream, and freshly grated nutmeg.
Cook for another 3–5 minutes, until the chicken is heated through and the tortellini are tender.
Taste and adjust seasoning as needed. Serve hot with shaved or grated Parmesan and fresh chopped parsley, if desired.