Step 1

Bring a large pot of salted water to a boil. Melt the butter in a medium Dutch oven over medium-low heat. Add the onion and cook, stirring occasionally, until softened, 5 to 6 minutes. Add the garlic and cook until sizzling, about 1 minute. Sprinkle in the flour and stir to coat the vegetables. Cook, stirring, until the coating is smooth but not browned, about 2 minutes.

Step 2

Add the chicken broth, heavy cream, 1 cup water and 1/2 teaspoon salt to the pot, and stir to combine. Adjust the heat so the soup is simmering and cook until slightly thickened, about 10 minutes.

Step 3

Meanwhile, add the fettuccine to the boiling water and cook until just al dente, 6 to 7 minutes, adding the broccoli to the pot in the last 3 minutes of cooking. Drain well, then stir the pasta and broccoli into the soup along with the chicken.

Step 4

Return the soup to a simmer and heat the chicken through, about 2 minutes. Stir in the parsley. Remove from the heat and stir in the parmesan and lemon juice; sprinkle with red pepper flakes, if desired.