In a dutch oven melt 2 tablespoons of butter over medium to medium-low heat. Add broccoli, onions, carrots and 1/2 teaspoon of salt. Stir, cover and cook until tender. About 12 minutes. This will depend on the size of your vegetables.

Meanwhile, add broth and half & half to a small sauce pan and warm on low heat. No need to boil, you just want the liquids warm.

Once the vegetables are tender, add in the remaining 4 tablespoons of butter, stir until melted. Sprinkle in the flour. Continue stirring until the butter has absorbed the flour and cook for 2 to 3 minutes.

Stir while pouring in the warm broth and half & half. Grate in the nutmeg.

Simmer uncovered over medium to medium-low heat for 20 to 25 minutes or until the soup has thickened.

For smaller pieces of broccoli, use a potato masher to smash the broccoli and break it up.

Turn the heat off and add in half of the grated cheddar cheese and heat through.

Taste and season with 3/4 teaspoon kosher salt (more or less to your preference) and 1/4 teaspoon freshly ground black pepper.

Ladle soup into bowls and top with a little of the remaining cheddar cheese.