Finely chop the onions and celery. Slice the carrots into thin matchsticks, and cut the broccoli into small florets.
In a Dutch oven, melt 4 tablespoons of butter and sauté the onions until soft. Add the celery and carrots, and cook until the vegetables are tender.
Stir in the minced garlic and cook for another minute until fragrant.
Pour in the broth, add the broccoli, and season with salt and pepper. Simmer for about 5 minutes, or until the broccoli is tender.
In a separate bowl, whisk together the heavy cream, milk, and flour. Add this mixture to the pot and cook over low to medium heat.
Turn the heat down to low and make sure the soup isn’t bubbling, and add in the cheese one cup at a time, stirring it in.
Enjoy, friends!