Place the chicken breasts, chopped onion, minced garlic cloves, and bay leaf into a large pot.

Pour in the water or chicken broth and bring to a boil.

Simmer until the chicken is fully cooked and tender.

Remove the chicken from the pot and set aside to cool.

Add the chopped celery and chopped carrot to the simmering broth.

Cut the cooked chicken into bite-sized pieces and return it to the pot.

Simmer until the vegetables are almost tender.

Add the dried egg noodles and continue simmering until the noodles and vegetables are fully cooked.

Season with salt and pepper to taste.

Stir in the shredded Monterey Jack cheese until melted and well combined.