Add the chicken broth, broccoli, and carrots to a heavy bottom soup pot. Bring to a boil, then reduce the heat to low and let simmer until the vegetables are fork tender, about 6-8 minutes. Add in the garlic powder and onion powder.
Let the liquid cool to below 150F before adding the cheese so it doesn't clump and sink to the bottom. Add in the cheese a handful at a time, making sure it is incorporated before adding more. When all of the cheese is incorporated, add in the heavy cream and the cream cheese.
Remove from the heat and season with salt and pepper to taste. The soup with thicken nicely as it sits. Serve with extra shredded cheese, if desired.
Notes
I used 4 cups of fresh broccoli, but you could use frozen if you like.
I like to use pre-shredded sharp cheddar. It incorporated into the soup perfectly.
Let the liquid cool a bit before adding the cheese. Liquid above 150F will cause the cheese to not incorporate because it breaks down the protein bonds. Add in the cheese a handful at a time and let it melt completely before adding more.