Heat oil in a large, deep stockpot.
Season chicken generously and once oil is hot, cook chicken until golden -about 5 mins.
Add the 1/4 c. parmesan cheese and cook 1 more minute. Plate the chicken.
In the same pot, add butter, shallot, and garlic.
Cook 3 minutes.
Add 4 cups water. Bring to a boil, add the pasta, and cook, stirring often, until the pasta is how you like it.
Stir in the cream, mustard, the 1/2 cup parmesan, baby broccoli (or spinach) and add in the chicken with any juices on the plates. Simmer a few minutes. Top with more parmesan for serving, if desired.