Thinly slice the onion. Add it to a pan with a drizzle of olive oil over medium-low heat. Stirring occasionally, allow the onion to caramelize while you prepare the rest of the dish.
Meanwhile, poach the chicken. Using thawed or frozen chicken (either one), add the chicken to a large pot and cover it with water. Add 1 teaspoon salt and any vegetable bits that you'd like to use (optional). Cover the pot, and bring the water to a boil then reduce to a simmer. Cook the chicken until done, 10 - 20 minutes depending on what cut of chicken you use.
While the chicken is cooking, finely chop the carrot and celery and mince the garlic.
When the chicken is cooked through, remove it to a plate to cool and strain the cooking liquid into a bowl.
In the same pot, boil the pasta to al dente and drain. While the pasta is cooking, stir the onion and shred the chicken with forks or fingers.
When the pasta is cooked and drained, add the butter and oil to the same pot over medium-high heat with the carrots. Stir and cook for 2 minutes, then add the celery and cook for 2 minutes more.
When the veggies are soft, add the garlic and lemon zest. Stir for one minute, then sprinkle the flour over the veggie mixture and stir to combine for one minute more. Add 2 cups of the reserved chicken cooking liquid, and bring to a bubble to thicken the mixture. Add more stock as needed to create a thin gravy.
To assemble, add the noodles, chicken, and caramelized onions to the pot with ½ teaspoon of seasoning salt. Stir together, and taste. Add more salt or seasoning salt if you'd like, and more chicken liquid to create enough sauce to coat all the pasta.
Serve topped with parsley leaves.