Grease a 9x13-inch baking dish.
Place the chicken, 4 tablespoons of the salt, and the bay leaf in a large Dutch oven.
Fill the Dutch oven with enough water to cover the chicken.
Bring the water to a boil over high heat.
Cover the Dutch oven and reduce the heat to medium-low.
Simmer until the chicken is tender and cooked through at 165 degrees F internally, about 1 hour.
Transfer the chicken to a plate, reserving the broth in the Dutch oven.
Cool the chicken completely, about 20 minutes.
Discard the bay leaf, skin and bone the chicken, and cut the meat into pieces.
Preheat the oven to 350 degrees F.
Transfer and reserve 1/4 cup of the chicken broth.
Bring the remaining broth to a boil in the Dutch oven over high heat.
Break the spaghetti into thirds and cook it in the broth until tender, about 12-15 minutes.
Drain the spaghetti well, discarding the broth it cooked in.
Return the spaghetti to the Dutch oven.
Melt the butter in a large skillet over medium-high heat.
Add the onion, the green pepper, the celery, and the garlic and sauté until tender, about 5 minutes.
Add the vegetable mixture to the spaghetti.
Stir together the cream of mushroom soup and the reserved broth.
Stir the soup mixture into the spaghetti mixture.
Stir the chicken, the diced tomatoes, the Worcestershire sauce, the hot sauce, and the black pepper into the pasta mixture.
Season the mixture with the extra salt.
Pour the spaghetti-chicken mixture into the prepared baking dish.
Top the pasta mixture with the cheddar cheese.
Bake until the cheese melts, about 15-20 minutes.
Serve.