Melt the light butter in a large soup pot or Dutch oven over medium heat. Add the diced onion and shredded carrots. Cook for 4–5 minutes, until the onion begins to soften.
Stir in the minced garlic and cook for about 30 seconds.
Sprinkle the flour over the vegetables and stir continuously for about 1–2 minutes. This cooks the flour and creates the base for the creamy soup.
Slowly pour in the chicken broth while whisking constantly to prevent lumps. Add the Italian seasoning, salt, pepper, garlic powder, and onion powder.
Break the lasagna noodles into bite-sized pieces and add them to the soup. Bring to a gentle boil, then reduce the heat and simmer for about 10 minutes, stirring occasionally.
Stir in the broccoli and continue cooking for another 5–7 minutes, or until the noodles and broccoli are tender.
Stir in the shredded rotisserie chicken and skim milk. Cook for about 3–4 minutes, until everything is heated through. Don't let the soup come to a hard boil after adding the milk.
Reduce the heat to low. Gradually stir in the shredded low-fat cheddar cheese until completely melted and the soup is creamy.
Taste and adjust the seasonings if needed. Serve warm.