As seen on Food.com (and elsewhere)
1 tablespoon melted butter
1⁄2 medium chopped onion
1⁄4 cup melted butter
1⁄4 cup flour
2 cups half-and-half
2 cups homemade chicken stock
1⁄2 lb. fresh broccoli (chopped into bite size pieces)
1 cup carrot, julienned
1⁄4 teaspoon nutmeg
8 ounces sharp cheddar cheese, grated
Salt and pepper
Saute onion in butter. Set aside.
Cook melted butter and flour using a whisk over medium heat for 3-5 minutes. Stir constantly and add the half & half.
Add the chicken stock. Simmer for 20 minutes.
Add the broccoli, carrots and onions. Cook over low heat 20-25 minutes.
Add salt and pepper. Can be pureed in a blender but I don't. Return to heat and add cheese. Stir in nutmeg.
Serve with crusty bread.
http://pattietierney.blogspot.com/2015/11/st-louis-bread-companys-broccoli-cheese.html