Make the Chicken Broth
In a large dutch oven pot, heat the oil and butter over medium high heat until the fat is shimmering hot.
Pat the chicken thighs' skin dry with a paper towel, then season generously with salt and pepper. Place the thighs skin-side down in the hot oil and sear for 3-4 minutes, until the skin is crispy and golden brown.
Flip the chicken over and sear the meat for another 3-4 minutes, until there is a golden brown crust. Remove them from the pan and place onto a plate.
Turn the heat down to medium and add the quartered onion, celery, carrots, halved garlic head, thyme sprigs, and bay leaves. Season with a teaspoon of kosher salt. Sear until the vegetables gain some color, for 3-5 minutes.
Pour in the cold water and the apple cider, then add the chicken thighs back to the pot.
Let the broth come to a simmer. Cover and simmer for 90 minutes.
After the 90 minutes are up, remove the chicken thighs with tongs to let cool enough to shred, and carefully strain the chicken broth into a wire mesh strainer lined with paper towels over a large mixing bowl. Try to keep the vegetables in the bowl so the fat and liquid fall into the paper towels (only if you're using the fat in the next steps).
Set aside. Transfer the fat from the paper towels into a small container, if using.
Make the Chicken Noodle Soup
Add the chicken fat back into the dutch oven and turn the heat to medium heat.
Toss in the diced onion, sliced celery, and sliced carrots into the pot. Give them a teaspoon of kosher salt, then sauté for 4-5 minutes to gain some brown color.
Add the broth back to the pot and let simmer for 10 minutes.
While the vegetables are simmering, shred the cooked chicken and discard the skin and bones.
After the 10 minutes are up, add the shredded chicken and egg noodles to the soup. Turn the temperature up to medium high and cook the noodles until al dente according to package directions.
Taste the soup and season with salt and pepper to taste.
Serve hot in soup bowls with crusty bread.