In a large pot, add oil along with onion, garlic, carrots, red bell pepper, and mushrooms and cook until vegetables are soft. Sprinkle vegetables with flour and cook, stirring constantly, for 2-3 minutes.
Slowly whisk in broth until smooth. Add in the Better Than Bouillon, Italian seasoning, rosemary, bay leaf, salt, black pepper, and Parmesan cheese and bring to a boil, then immediately reduce heat and simmer, stirring often so cheese doesn't stick to the bottom of the pot, uncovered, for 20 minutes.
Add in the tortellini. Simmer, continue stirring occasionally, until tortellini is almost al dente. Stir in the chicken and cream. Continue to simmer until chicken is heated through.