This dish is a one pot wonder from start to finish. Instead of using a saute pan for the chicken, a pot to blanch the broccoli and a third pot to boil pasta, we do it all in one
Bring a large pot of salty water to boil and cook spaghetti according to package instructions. (Subtract a minute of cooking time for al dente.)
Add broccoli to the boiling water with pasta when there are 2 minutes left of cooking time. Drain pasta and broccoli, reserving 1 c starchy cooking liquid.
Lightly brush chicken breast with 1 tsp of olive oil, sea salt and red chili flakes.
Grill chicken breast until browned, about 4 minutes per side.
In the same pot that you cooked the pasta and broccoli, heat remaining 1 tbs of olive oil over medium heat.
Add garlic and cook for 30 seconds.
Add in pasta, broccoli and cooked chicken (cut in cubes).
If mixture seems dry, add in a bit of the reserved starchy cooking liquid until you reach desired consistency.
Season with lemon juice, zest and Parmesan cheese.
Check for seasoning and add more salt or pepper if needed.