Cook skinless chicken breasts by your preferred method if you do not have any already cooked.
In a large pot add water, place the large pot of water on the stove and bring to a boil.
Once the water is boiling add in the dry pasta and cook for 8-10 minutes. Check the package instructions for how long to cook for al dente pasta. Drain noodles with a strainer once it is done cooking and return to the pot.
While the pasta cooks preheat the oven to 350°F.
Shred the white cheddar cheese or chop it into pieces and set it aside.
Cut the broccoli into small pieces and set it aside.
Cut the chicken into small pieces and set it aside.
In a medium sauce pan over medium heat add the butter and melt butter. Once the butter is melted add the flour and whisk until combined.
Add in the milk a little bit at a time and whisking each time until smooth until all the milk is added.
Bring the milk and flour mixture to a boil and add a pinch of salt and a pinch of pepper. Turn the heat down to low and let cool slightly.
Pour the white sauce into the cooked pasta.
Add the cheese and stir until it is mostly melted.
Add in the cooked chopped chicken and the chopped broccoli. Mix well to combine everything.
Spray a casserole dish or baking dish with nonstick cooking spray and pour the pasta mixture into it.
Sprinkle the top of the pasta with the Italian bread crumbs.
Slice the remaining 1/4 stick of butter into thin pieces and place on top.
Bake in the oven for 20-30 minutes until the breadcrumb crust has browned.