Combine egg, milk, and salt in a small bowl; stir together with a fork. Add enough flour to make a stiff dough.
Roll the dough into a ball and let it rest for 5 minutes. Use a rolling pin to roll the dough out very thin on a lightly floured surface. Use a pizza cutter to cut them into strips that are about 1/2 inch wide.
Place the noodles on a wire rack to dry. Let them sit for about an hour, then cut to desired length. (Don’t stress too much about the drying time. I have let mine dry for up to 4 hours, or as little as 30 minutes. Just adjust the cooking time—the longer they dry, the longer they take to cook.) No stress!
For soup:
Combine all broth ingredients in a large pot. Bring to a boil over medium-high heat. Reduce heat to low and simmer, covered for 30 minutes, or till chicken is done. Remove the chicken and strain the broth. (This will remove all the spices, so you will add more.)
Return broth to pan and add carrots, onion, celery, garlic, and additional seasonings. Simmer for 10-15 minutes. While it is simmering, shred the chicken.
Turn the heat up to medium and bring to a rolling boil. Stir the noodles into the boiling broth, then add the shredded chicken meat and peas. Cook for about 8-10 more minutes or till noodles are al dente. Taste broth and adjust seasonings to your taste. Remove bay leaves before serving.
Notes
You can use a whole chicken in place of the chicken breasts, you will just need to remove the chicken bones and skin before shredding.
If you have leftovers, the noodles will soak up lots of the broth. Don’t panic, just add extra water or chicken broth