Add the olive oil, onions, carrots, and celery to a large soup pot over medium-high heat. Cover with the lid slightly open, and cook for 8 to 10 minutes, stirring occasionally. You want the vegetables to become tender and aromatic, which will form the flavorful base of the soup.
Add the mushrooms and garlic to the pot. Cook for a few more minutes, with the lid off, stirring occasionally. The mushrooms will release their moisture, intensifying the flavors and adding depth.
Add the flour and give it a good stir. Let it cook for about a minute to remove the raw flour taste. This will help thicken the soup.
Add the chicken broth, water, chicken, and Italian seasoning. Stir well to combine all the ingredients, ensuring the broth is rich and flavorful.
Increase the heat to high, and once the soup is boiling, add the tortellini. The tortellini will soak up the delicious broth as it cooks.
Reduce the heat to medium or even lower to maintain a gentle boil, and cook for 5 minutes. This allows the tortellini to cook through while the flavors meld perfectly.
Add the heavy cream and spinach and let the soup heat through. Stir until the spinach is wilted and the soup is creamy.
Season with salt and pepper as needed, adjusting to your taste. Serve immediately, enjoying every comforting spoonful.