In a large pot of salted boiling water, cook the medium shells pasta according to package instructions until al dente. In the last 3 minutes of cooking, add the chopped broccoli to the pot. Drain and set aside, reserving 1 cup of pasta water.
While the pasta cooks, season the chicken breasts with 1 teaspoon of salt, pepper, and 1 teaspoon of Italian seasoning. In a large skillet over medium heat, melt 1 tablespoon of butter. Add the chicken breasts and cook for 5-7 minutes on each side until golden brown and cooked through. Remove from the skillet and let them rest for a few minutes before slicing into bite-sized pieces.
In the same skillet, melt the remaining butter over medium heat. Add the minced garlic, onion powder, garlic powder, and dried thyme (if using). Sauté for about 30 seconds, until fragrant. Pour in the chicken broth and scrape the bottom of the skillet to release any browned bits. Bring to a simmer.
Reduce the heat to low and stir in the heavy cream, the remaining salt, and Italian seasoning. Allow the sauce to simmer for 2-3 minutes until it thickens slightly.
Add the cooked pasta and broccoli to the skillet, tossing to coat everything in the creamy sauce. If the sauce is too thick, add a little reserved pasta water until you reach the desired consistency.
Stir in the Parmesan cheese until melted and well combined. Taste and adjust seasoning as necessary. Serve hot, garnished with fresh parsley if desired.