Prep carrots (2 medium), onion (1/4 large onion), and garlic. Cut broccoli florets off of the stem and dice as fine as you would like. I like a chunky soup, but if you prefer a smoother texture, be sure to dice everything up really fine.
In a large kettle, add butter, carrots, onion, and garlic. Saute over medium heat for about 3 minutes. Add flour to the mixture, stir well and let it cook another two minutes.
Add the chicken broth very slowly, while stirring constantly. You want the flour to smoothly incorporate into the broth. If you dump the broth in, you will get lumps.
Add the pepper, garlic powder, and Italian seasoning. Bring to a simmer.
Add the broccoli to the broth mixture and let it simmer until the broccoli is tender - about 5-7 minutes depending on how finely it is diced.
Add the shredded cheddar and stir well to incorporate the cheese while it melts.
Remove the soup from heat and then stir in the cream. Serve with fresh bread and enjoy!