1.Put a pot of water with salt on to boil for your pasta. Boil pasta using box instructions. Drain pasta and keep 1/2 cup of pasta water.
2.Meanwhile, heat butter in a skillet over medium heat. Add the onion and sauté for 2 minutes, season with some salt and pepper. Then add the garlic and sauté for another minute.
3.Next whisk in the flour, and let cook for 1 minute. Then whisk in the milk. Bring to a slow and steady bubble, and whisk constantly letting the mixture thicken for 1 minute. Then add the goat cheese and parmesan and whisk to combine. Stir the sauce until the cheese has melted.
4.Whisk in the lemon juice, then stir in the chicken and keep warm over low heat.
5.Rinse your broccoli with water, then place the broccoli in a microwave safe bowl and microwave it for 2 minutes. Drain off any excess water and add the broccoli to the sauce.
6.Stir reserved pasta water into the sauce and add drained pasta. Let it warm through for 1 minute. Then serve the pasta topped with a touch of lemon zest.