Heat 2 tablespoons olive oil and 2 tablespoons butter on a medium-heat in a large skillet.
Add 1 pound chicken breasts chunks, chopped 1 small onion, minced 4 garlic cloves and cook for 2 minutes.
Now, add ½ teaspoon salt, ¼ teaspoon freshly ground pepper and cook for 3-4 minutes until chicken turns opaque.
Add ¾ teaspoon dried thyme, ¾ teaspoon dried oregano, ½ teaspoon paprika, ¼ teaspoon red pepper flakes, 1 tablespoon lemon zest - mix and cook for 30 seconds.
Pour 2 ¾ - 3 cups low sodium chicken stock, 1 cup heavy cream and stir. Bring to a boil.
Stir in the 3 cups Conchiglie Rigate pasta, reduce the heat to medium-low (simmer).
Cover with lid and cook for 9-10 minutes.
Now, add 3 cups broccoli florets, ¼ cup cream cheese and stir. Put back the lid and let it cook for 3 minutes or until broccoli is just tender and pasta is cooked.
Stir in the 1 tablespoon lemon juice, grated ½ cup parmesan cheese and shredded ¾ cup cheddar cheese.
Sprinkle fresh chopped parsley and serve. Enjoy!