Cook the broccoli florets in water until tender, drain and set aside.

Melt one Tablespoon of butter in a saute pan, add the onion and minced garlic. Saute until onion is translucent, set aside.

Over medium heat, melt 3 tablespoons of butter in a 4 quart metal sauce pan. Add 3 Tablespoons of flour, whisk the flour and butter together and let come to a boil. Boil and whisk for 2 minutes to remove the flour taste. Slowly add four cups chicken broth to the pan while whisking. Whisk until broth comes to a slow boil and thickens slightly. Add the sauteed onion and garlic and cooked broccoli florets to the pan. Stir to combine. With the heat on low, continue to cook the mixture until broccoli is heated through. Turn the burner off, remove the pot from the stove. Slowly add cheddar cheese by cupfuls while stirring the soup. When it has all melted, add 1/2 cup cream to the pan. Stir to incorporate. Add 1 Teaspoon garlic powder if the soup requires it, add salt and pepper to taste. Serve immediately, refrigerate leftovers.