Preheat oven to 350°F. In a large pot of salted boiling water, cook pasta according to the package instructions. Once al dente, drain and set aside.
Shred the cooked chicken breasts or the rotisserie chicken with a fork.
In a large bowl add the cooked pasta, the shredded chicken, and the following ingredients - diced onion, bell pepper, celery, cream of mushroom soup, cream of chicken soup, salt, pepper, and chicken broth. Gently mix everything together. Do not add the butter or cheese at this step.
Next, add the butter to a 9x13-inch baking dish and place it in the preheated oven so the butter can melt. It should take approximately 3-4 minutes. Once the butter is melted, carefully remove the baking dish from the oven.
Add the chicken tetrazzini mixture to the buttered baking dish and spread it out evenly. Bake the casserole in the oven for 40 minutes. The sides will be bubbling at this point.
Carefully remove the casserole dish from the oven and add the sharp cheddar cheese on top. Place the dish back in the oven for 5 minutes or until the cheese is melted.
Once done remove the chicken tetrazzini from the oven and allow it to rest for 5-10 minutes, enjoy!