I'm a large skillet or pot with a tight fitting lid, heat the oil and butter over med-high heat. Once it's melted and sizzling, add the chicken pieces and season them with 1/4 tsp. each of salt and pepper and the onion powder. Cook just until they have browned on the outside, just about 3-5 minutes...don't worry about them being cooked through, as they will continue to cook in the pan. Add the garlic to the pan and cook just until fragrant, a minute or so.

Pour in the broth and cream. Once it starts to come to a low boil, stir in the pasta, remaining salt and pepper and the nutmeg. Cover the pan with its lid and reduce the heat down to medium-low. Allow this to simmer, stirring often, for about 10 minutes.

After 10 minutes, stir in the broccoli florets and cover again. Continue to cook an additional 5 minutes, until the broccoli is tender and the pasta is al dente. A lot of the liquid should've been absorbed, but it should still be creamy. Remove the pan from the heat and immediately stir in the parmesan. Let it sit to thicken for 5 or so minutes, then serve.