Bring a large pot of salted water over high heat for the egg noodles. Discard the skin from the chicken and remove the meat from the bones. Shred the chicken meat with your fingers or two forks and reserve.
Place a large skillet over medium-high heat with the EVOO. Add the onion, carrot and celery to the pan, and cook until the veggies begin to get tender, 3-4 minutes. Toss the zucchini into the pan along with some salt and freshly ground black pepper, and cook another 2-3 minutes until all the veggies are tender.
While the veggies are cooking, drop the noodles into the boiling water and cook to al dente according to package directions. Drain the noodles and return them to the pot they were cooked in. Add the butter and parsley to pot and give everything a good toss to melt the butter and coat the noodles.
Add the shredded chicken and peas to the pan with the veggies and cook until the chicken is heated through.
To serve, spoon some noodles into bowls and top with the chicken and veggie mixture.