Melt the butter in a large Dutch oven over medium heat and add the olive oil. Add the onion, celery and carrots and saute until soft, about 4 minutes. Season with salt and pepper, to taste. Stir in the chopped garlic and saute until fragrant, 1 minute more. Whisk in the flour and stir frequently until it coats the vegetables and makes a paste. Cook until it reaches a pale blonde color, about 2 minutes. Gradually whisk in the chicken stock, making sure there are no lumps. Add the bay leaf, hot sauce, and Worcestershire and season with salt and pepper, to taste. Let the soup simmer for 15 minutes to thicken and develop the flavors.
Reduce the heat and add the chicken and the noodles. Do not boil the chicken or it will become tough. Add the peas and the dill and simmer gently for 10 more minutes.
Taste for seasoning and add more salt and pepper, if needed. Ladle the soup into serving bowls and serve.