Preheat oven to 375 F and get 9x13 baking dish ready. Add chicken and broccoli to it. Set aside.
In a large pot, add water and bring to a boil. Add a pinch of salt and pasta, cook until al dente. Drain and add to the dish with chicken and broccoli.
Preheat large skillet on medium heat and add butter to melt. Add garlic and saute for 1-2 minutes or until fragrant, stirring frequently.
Add chicken broth, milk, cornstarch, smoked paprika, salt, pepper and whisk until smooth. Bring to a boil, reduce heat to low and simmer for a 1-2 minutes until sauce has thickened a bit.
Remove skillet from heat, add Parmesan cheese and whisk until smooth. Pour over pasta, chicken, broccoli and stir.
Add dollops of Greek yogurt and stir well to combine until yogurt is incorporated into the sauce. Then sprinkle mozzarella cheese on top.
Bake uncovered for 20-25 minutes. Remove from the oven, garnish with parsley and serve.
Notes
Store: Store leftovers in an airtight container in the fridge for up to 5 days.
Reheat: Reheat in a microwave or on the stove with a bit of water or broth until heated through.
Freeze: I do not love to freeze pasta because it changes texture but you can, if you wish. Freeze in an airtight container for up to 3 months.