In a large Dutch oven or stockpot, heat the olive oil and melt the butter over medium heat. Add the chopped onion, carrots, and celery. Cook, stirring occasionally, for 6-8 minutes, until the vegetables have softened.

Stir in the minced garlic, dried oregano, and dried thyme. Cook for 1 minute more until fragrant.

Sprinkle the all-purpose flour over the vegetables and stir constantly for 1-2 minutes to cook out the raw flour taste. This will create a roux that helps thicken the soup.

Slowly pour in the chicken broth, about one cup at a time, whisking continuously to prevent lumps and create a smooth base.

Bring the soup to a simmer, then reduce the heat to low. Let it gently simmer, partially covered, for 10 minutes to allow the flavors to meld together.

Stir in the heavy cream, shredded cooked chicken, and the uncooked refrigerated tortellini. Increase the heat to bring back to a gentle simmer. Cook for 5-7 minutes, or until the tortellini is cooked through and floats to the surface (check package directions for exact timing).

Turn off the heat. Stir in the fresh spinach and the grated Parmesan cheese. Continue stirring until the spinach has wilted and the cheese has melted completely into the soup.

Taste the soup and season with salt and black pepper as needed. Ladle the hot chicken tortellini soup into bowls, garnish with fresh parsley and extra Parmesan cheese, and serve immediately.