Start off by steaming the broccoli in 1 inch of boiling water for 3-4 minutes until al dente. You want the broccoli to be slightly undercooked since it will cook more in the sauce.
Put a pot of salted water on to boil to cook the pasta.
Meanwhile, work on the sauce. Melt the butter in a saucepan and whisk in the flour. Then whisk in the milk and bring to a slow and steady boil for 1 minute, letting the sauce thicken. Once the sauce has thickened, whisk in the lemon juice, goat cheese, and parmesan, stirring until the cheese melts. Season with salt and pepper. Add the broccoli and chicken to the sauce, stir to combine, and keep warm on low heat.
Next cook the pasta. Fresh pasta will cook in 1-3 minutes. Before you drain the pasta, take ½ cup of water from the pot and stir it into the sauce.
Drain the pasta and pour it into the sauce and stir to combine. Let the pasta simmer in the sauce for 1-2 minutes while the pasta soaks it in. Then serve the pasta.