Prepare all the ingredients: divide the broccoli into florets, cut the chicken breast into 1-inch (2.5 cm) cubes, chop the garlic very finely, grate the mozzarella and parmesan cheese.
Cook the pasta and broccoli: Cook the pasta al dente (it should have a bite to it) and steam (or cook) the broccoli. I like to cook the pasta in a pot and steam the broccoli in a sieve above the pot (see the photos in the post). So there's a pot with pasta, a sieve with broccoli florets hung above the pot, and all of that is covered with a lid. Fusilli pasta, that I have used, needs to be cooked for 10 minutes and the broccoli needs to be steamed for 8 minutes. While the pasta is cooking, cook the chicken and prepare the sauce.
Cook the chicken: Season the chicken with salt and pepper and toss with flour. Heat the oil over high heat in a big frying pan. Once hot, add the chicken pieces in an even layer. Don't stir for the first 2 minutes (to let the chicken brown), then cook, stirring until the chicken is cooked through (no longer pink inside). Transfer the chicken to a plate.
Make the cheese sauce: Add the butter to the pan, when it's sizzling add finely chopped garlic, dry basil, and onion powder and cook, stirring, over medium heat for a minute.
Add all 4 kinds of cheese and milk to the pan and cook until the cheeses are melted and the sauce has thickened (if it's too runny, just cook it a little longer, stirring from time to time). Season the sauce with salt, pepper, and lemon juice.
Assemble: Add the chicken back to the pan, add the cooked pasta and steamed broccoli. Stir everything together. Season a little more with salt, pepper and lemon juice, if necessary.
You can garnish the dish with grated parmesan cheese, chopped parsley, and toasted flaked almonds, if you wish.
Enjoy!