If you bought a fresh head of broccoli, be sure to cut of the florets and remove the massive stalk. (The stalk can be saved for vegetable stocks)

Melt the butter in a large sauce pan on medium heat.

Saute the onions until soft.

Add the flour and cook out for a few minutes until golden.

Add the chicken stock and the half and half. Stir to combine them well.

Add broccoli and carrots. Simmer for about 20 minutes on low. Salt and pepper to taste

Blend 1-2 cups depending on your desired consistency (I like it less chunky, so I always do 2). return that to the pan.

Add the cheese a bit at a time, constantly stirring to melt all the cheese (I find it important to grate my own cheese because the pre shredded stuff come coated in starches that throw off the whole flavor)

Add the nutmeg and mix well

Serve and enjoy