Melt butter over medium heat in a Dutch oven or large pot.
Add onion, celery, and carrots and cook until soft, about 5 minutes.
Add garlic and cook 1 minute. Season with salt.
Sprinkle flour over veggies and stir and cook for 1 to 2 minutes.
Gradually stir in chicken broth. Add bay leaves, Worcestershire sauce, and Tabasco.
Bring to a simmer and simmer for 10 minutes, stirring occasionally.
Add egg noodles and cook 5 minutes.
Stir in half-and-half, chicken, and peas and continue to cook just until noodles are cooked through, about 5 more minutes.
Stir in pepper and dill and serve.