Cook the pasta in a large pot of salted water, according to the package instructions to al dente. During the last 3 minutes of cooking, add the broccoli florets.
Drain pasta and broccoli, rinse with cold water and return to the pot. Add the shredded chicken and set aside.
Heat the oven to 375℉ and prepare a 9 x 12 baking dish with non-stick cooking spray or butter.
Melt the butter in a saucepan over medium heat. Add the flour and stir constantly for 2 minutes, being sure not to let it brown. Whisk in the milk until thoroughly incorporated and smooth and bring to a simmer. Turn the heat down and allow to simmer for 5 -6 minutes, until the sauce is thick enough to coat the back of a spoon. Turn off the heat and stir in the shredded cheese. Taste for seasoning and adjust as needed.
Pour the cheese sauce over the pasta, broccoli, and chicken. Toss to coat, making sure that the sauce is evenly distributed. Pour the pasta mixture into the prepared baking dish.
In a small bowl, combine the melted butter, panko breadcrumbs, seasoning salt, and thyme. Sprinkle this mixture evenly over the mac and cheese. Bake for 15-20 minutes until the sauce is bubbling and the top is golden brown.