Cut your broccoli into 1 - 2 inch chunks.
Remove the tough outer layer from the stalk and cut this as well.
Boil your broccoli in a large pot until it’s tender but still has a bite to it.
While you boil your broccoli, dice your sweet onion.
After dicing your onion, add the onion to 4 tbsp of butter in a large pot on medium heat.
Drain the broccoli and set aside.
Once the onion is soft and translucent, add in the garlic, and stir.
Next, pour in the broth and milk.
Add in the sour cream, and whisk.
Stirring constantly, slowly add the cheese.
Keep stirring until all of the cheese has melted.
Add the broccoli and shredded carrot.
Add salt and pepper to taste.
Pour 1 cup of cold water and 1 ½ tbsp of cornstarch into a glass measuring cup.
Add 1 more tablespoon of cornstarch at a time to this mixture until your mixture is thick but still liquid.
Slowly pour the mixture into your hot soup, stirring constantly.
Add cornstarch mixture until your soup has reached the desired consistency.
Cook soup for 30 minutes, stirring occasionally.