Melt 3 Tablespoons butter in a large pot.
Finely chop the onion and garlic cloves and sauté in the butter until tender.
Stir in the 6 Tablespoons flour.
Gradually whisk in the 6 cups chicken broth (I use 6 bouillon cubes and 6 cups of water), 1 cup of heavy cream, 1 teaspoon salt, plus an additional 2 cups water and stir and heat over medium heat until thickened.
Add in the package of frozen broccoli and 9oz of fettuccine and cook until tender. (Note: you will have to look at suggested boiling times on both the pasta and the broccoli packages and adjust when you put them in the pot, depending on how long your specific brand is supposed to cook. The Buitoni brand of fettuccini that I used only had to cook for 2 minutes, so I added it after the broccoli had already boiled for a couple of minutes).
Stir in the cooked chopped chicken, 1/2 cup parmesan cheese, and 1 Tablespoon of lemon juice.
Remove from heat.
Add Italian seasoning (or fresh parsley) and salt and pepper to taste.