Melt 4 tablespoons of butter in a large pot over medium heat. Once it's melted, add the all of the onion, garlic, and 1/4 cup of bacon crumbles. Stir and cook them until the onion starts to soften, about five minutes or so.
Add the chopped broccoli and stir. Cook the broccoli for five minutes and then sprinkle 1/4 cup of flour and 1/4 teaspoon of salt over the top. Stir until flour coats it all evenly.
Add 8 cups of chicken broth, stir, and bring the broth to a simmer over medium-high heat. Simmer the soup for 10 minutes.
Adjust the heat to medium-low and stir a 1/2 cup of cream into the soup followed by the chicken.
Whisk the cheese into the soup in a few batches, whisking until each addition is melted before adding more. Once the soup is creamy and the cheese is fully melted, ladle it into bowls and enjoy.
Notes
If you want to fry bacon instead of using packaged bacon crumbles, cook it first and then drain the fat from the pan. You will need about 3 to 4 ounces of raw bacon to get 2 ounces crumbled.Roughly chopping the broccoli adds nice texture to the soup, but you can finely chop it if you prefer.The soup is best when it's made, but leftovers will keep in the refrigerator for a few days. I don't recommend freezing the leftovers.