Heat olive oil on medium heat in a large pot.
Add chicken breasts, season with salt and pepper, and allow the chicken to brown on one side.
Flip chicken, then add onions and garlic as the second side browns.
Once the chicken has browned on both sides, add chicken broth, water, and pasta to the pot.
Stir all ingredients, cover the pot with a lid, and bring to a boil.
When it begins to boil, uncover and stir.
Bring the heat to low, stir, then cover and let simmer for 20 minutes.
After 20 minutes has passed, uncover and add in the broccoli.
Stir continually as the broccoli steams until the rest of the liquid evaporates.
Add milk and cheddar cheese and stir until the cheese melts and you have a smooth cheese sauce.
Add salt and pepper (to taste), cayenne, and nutmeg.
Stir once more, then you're ready to serve.
Enjoy!