Heat the butter in a large pot over medium-high heat. Add in the onion and carrots and sauté until they're soft. Add in the garlic and cook for another minute.

Add in the flour, dijon mustard, paprika, nutmeg, salt and pepper and stir together until you can no long see the flour. Cook for a minute.

Pour in the broth and stir until evenly combined. Stir in the milk and bring the soup to a simmer.

Lower the heat to medium and add in the broccoli and cheese. Stir until the cheese is melted and the broccoli is tender, about 3-5 minutes depending on how cooked you want the broccoli. Taste for seasoning and serve.