Preheat your oven to 425 degrees Fahrenheit. Spray a 9 by 13 inch baking dish with cooking spray. Set aside.
Bring a large pot of water to a roaring boil. Salt the water with 1 teaspoon kosher salt. Add the pasta and cook according to the time indicated on the box, boiling for the shorter amount of time on the box if there is a range. Reserve 1 cup of pasta water before draining.
16 ounces small shell pasta
Melt the butter in a large skillet over medium low heat. Add the garlic and onion, and saute until both are soft, 5 to 7 minutes.
6 tablespoons unsalted butter, 1 small yellow onion, 3 garlic cloves
Whisk in the flour. Cook until there is no white from the flour visible to ensure that you cook out the flour taste. Slowly whisk in the chicken stock. I like to whisk in about 2 tablespoons at a time to start, adding more after what you just added was absorbed. The more you add the faster you can add it. The whole process should take less than 1 minute.
1/3 cup all purpose flour, 1 cup low sodium chicken stock
Whisk in the pasta water and the milk. Season with salt, parsley, basil, and pepper. Bring to a boil. Add in the broccoli and then reduce the sauce to a simmer, cooking for 5 minutes. Stir occasionally to prevent the sauce from burning. Taste the sauce and add more salt and/or pepper to taste.
1 cup milk, 1 teaspoon kosher salt, 1 teaspoon dried parsley, 1 teaspoon dried basil, 1/4 teaspoon black pepper, 4 cups broccoli florets
Add the cooked pasta, cooked chicken, 1 1/2 cups of cheese, and sauce mixture to the baking dish. Stir to combine. Top with the remaining cheese.
3 cups cooked chicken, 3 cups cheddar cheese
Bake for 10 minutes (uncovered) or until the cheese is melted and bubbly.