In a large pan, heat the butter over medium heat and add the garlic when melted. Cook for 3-4 minutes.
Gradually whisk in heavy cream and bring to a simmer.
Reduce heat to low and simmer for 5 minutes, or until slightly thickened, stirring occasionally.
Remove from heat and stir in Parmesan cheese.
While the sauce simmers, warm the pre-cooked chicken in the microwave until heated through.
Cook fettuccine noodles according to package directions.
While the pasta cooks, steam the broccoli until it is tender-crisp, about 3-5 minutes.
Drain the pasta, reserving ½ cup of pasta water.
Add pasta, warmed chicken, and broccoli to the Alfredo sauce. Toss to combine, adding pasta water if needed to loosen the sauce.
Serve immediately with additional Parmesan cheese, if desired.
Notes
To store leftover chicken Alfredo, start by letting it cool completely to room temperature. Then, transfer it to an airtight container, either glass or food-safe plastic for 3-4 days.