In the same medium saucepan or in a Dutch oven, melt butter over medium-low heat and whisk in flour for about 1 minute or until roux is slightly bubbly.
Whisk in chicken broth and half and half and continue to cook over medium-low heat until thickened, whisking constantly.
Add in sauteed onions and carrots with the chopped steamed broccoli and cheddar cheese, stirring until cheese is melted.
Stir in salt, pepper and smoked paprika and simmer over low heat for about 5 minutes. Remove from heat.
Serve immediately and garnish with grated nutmeg, extra chopped broccoli and more cheddar cheese.
Refrigerate leftovers promptly.
Recipe by My Dragonfly Cafe at https://mydragonflycafe.com/broccoli-cheddar-soup/