Cook tortellini according to package directions. Set aside
Cook chicken and either shred or cut into chunks.
Heat olive oil and 1 tbsp butter in a large pot over medium-high heat. Add onion, carrots, celery and mushrooms and saute until onions are translucent and carrots/celery are soft. Then add garlic and saute 1 minute longer. Add in chicken broth, oregano, bay leaves and thyme and season with salt and pepper. Bring to a boil. Reduce heat to medium-low, add in chicken chunks, cover pot with lid and allow to simmer for 10 - 15 minutes.
While broth mixture is cooking, melt butter in a medium saucepan over medium heat. Add flour and cook, whisking constantly for 1 minute. While whisking vigorously slowly pour in milk. Season with salt and pepper and bring mixture just to a light boil, stirring constantly. Add cheese blend. Remove from heat and set aside.
Add in white sauce to the broth mixture, stirring until incorporated. Let cook on low for 5-7 minutes, stirring frequently. Add cooked tortellini and spinach. Continue to cook on low until the spinach is adequately wilted (about 2 minutes). Remove bay leaves.