Heat the oil over medium heat in a 12 inch cast iron cast iron skillet.
Sauté the onion for 5 minutes, until soft and fragrant. Add the garlic. Cook 2 minutes. Mix in the lemon juice.
Add the broth, milk and broccoli. Bring to a boil. Add the pasta making sure it's all submerged in the cooking liquid.
Cover the skillet and simmer the pasta for 8 minutes. Remove the lid, stir and continue to cook 8-10 minutes or until the pasta is done to your liking. Mix in the cheddar cheese in the last two minutes of cooking. Season with salt and pepper to taste.
Top with parsley and green onion. Serve immediately.