Add the butter, onion, and celery to a pot and sauté for 4-5 minutes.
Stir in the garlic and flour. Cook for about 2 minutes, breaking it up with your spoon/stirring it as you go along to cook the raw flour taste out.
Slowly whisk in the chicken broth until all the flour has dissolved/there's no lumps.
Stir in the cream, Worcestershire sauce, and salt. Increase the heat to high and bring the soup to a boil.
Stir in the pasta, then reduce the heat so it's simmering but not boiling rapidly (medium-low heat works with my cast iron pot & gas stove). Cover the pot with the lid slightly ajar.
Let the soup simmer for about 15-20 minutes or until the pasta has cooked, stirring fairly often so it doesn't stick to the bottom of the pot. If the soup looks like it's becoming too thick, add the 1/2 cup of water (or even more if needed).
Turn the stove off, and stir in the cheddar gradually.
Season with pepper and extra salt if needed.