In a large pot, cook pasta according to the instructions on the package. In the last 3 minutes of cooking, add broccoli. When fork tender, drain pasta and broccoli. Set aside.
In a small bowl, combine salt, garlic powder, onion powder and black pepper. Add chicken pieces to the rub tossing to coat.
Add olive oil to a skillet and heat over medium-high heat. Brown chicken on all sides, approximately 4 to 5 minutes total. Remove from heat and set aside.
In a large saucepan, melt butter. Once melted, add flour and cook for 1 minute, whisking constantly.
Whisk in milk, chicken broth and remainder of ingredients: garlic powder, black pepper, salt and cheddar cheese and stir until the cheese is melted.
Bring to a simmer and cook until bubbling and thick, approximately 5 minutes. Remove from heat and add in the pasta, broccoli and chicken. Stir to combine and cook for another 5 minutes. remove from heat and serve.