
Preheat the oven to 350℉ (180℃).
Season chicken cubes with salt, followed by salt-free Cajun Creole seasoning. Stir until thoroughly combined.
Heat oil in a large skillet, stir in the chicken, and cook for 3-5 minutes or until slightly browned.
Add minced garlic, stir for about a minute, followed by chopped onion and thyme, and cook until onions wilted—about 4 more minutes. Then remove and set aside.
Heat a 10-inch oven-safe skillet and add butter. As soon as butter melts, whisk in the flour. Continue whisking until the flour is thoroughly mixed with butter, then cook for about a minute.
Slowly add chicken broth, a little at a time, followed by the milk; you don't want the mixture to form lumps. Bring to a simmer, then turn the heat down to medium so it simmers gently and slightly thickens into a cream sauce (5-6 minutes)—season with salt and pepper to taste.
Turn off the heat, then stir in the pasta, broccoli, and about a cup of cheese, chicken mixture, and Creole seasoning. Adjust seasonings to your liking with salt and pepper, then top with the remaining cheese.
Bake, uncovered, at 350°F (180℃) for 15 minutes or until heated through.
Allow to cool slightly. Serve hot and garnish with chopped parsley if desired.