Begin by shredding the meat from the bones and skin on your rotisserie chicken. Reserve the meat for later and place it in the fridge. Place the bones and skin in a large stockpot.
To the bones, add the onion, carrots, celery, garlic, parsley, thyme, bay leaves, salt, and peppercorns. Cover everything with 8 cups of fresh water and bring to a simmer.
Keep the stock at a bare simmer, stirring frequently, for at least 4 hours, up to 8 hours. The longer you cook it, the more flavor it will have. Keeping it at a bare simmer will make for clear, non-cloudy stock.
Once the stock has cooked for as long as you have, strain the solids from the liquid. Discard the solids and reserve the stock.
Rinse out the stockpot and place it back over medium heat.
Melt the butter and oil together in the stockpot and add the chopped onions, carrots, and celery.
Cook for 8-10 minutes until the veggies soften and begin to brown.
Add the garlic and then deglaze the pan with the Homemade Chicken Stock. Bring to a simmer and step away to make the noodles.
To a bowl, add all ingredients and lightly mix with your hands. Begin to knead in the bowl until a firm mass has formed. Flour a work surface well and dump the dough out. Knead for a few minutes until the dough is smooth, soft, and cohesive.
Cut the dough in half and place one half under a damp towel.
Roll out the other half using a floured rolling pin to about ⅛-inch thick. Using a pizza cutter, slice uniform noodles about ½-inch by 2 inches long. Place the noodles into a floured mound and repeat with the other half of the dough.
Add the noodles to your boiling stock. Cook for 15 minutes, allowing the noodles to cook through fully.
Meanwhile, shred the chicken meat from earlier and add it to the soup to warm through. Also, add the frozen peas to warm.
While the noodles cook, mix the oat milk with the cornstarch until no lumps remain. A few minutes before the noodles are tender, add the oat milk mixture and allow the soup to bubble and thicken. Sprinkle the fresh thyme over the top.
After 5 minutes and once the noodles are cooked, taste for seasoning and add any salt or pepper as needed.
Serve, garnishing with optional chopped parsley.