Heat the olive oil and butter in your stockpot over medium heat until melted and shimmering. Add the chopped yellow onion and sliced shallots. Sauté for about 5 minutes until they soften and become translucent. Then, stir in the chopped garlic, celery, and carrots. Cook for another 5 minutes, allowing the vegetables to release their flavors.
Toss in the fresh thyme leaves, chopped rosemary, and crushed fennel seeds. Season generously with salt and black pepper. Stir everything together and let the herbs toast slightly for about 2 minutes to deepen their aroma.
Add the 8 cups of chicken bone broth to the pot. Increase the heat to bring the mixture to a gentle boil. Once boiling, reduce the heat to a simmer.
Add the boneless chicken breasts or thighs to the simmering broth. Cover the pot and let the chicken cook through, about 15-20 minutes, depending on thickness. You can check doneness by cutting into the chicken; it should be opaque and easily shreddable.
Remove the chicken from the pot and shred it with two forks. Return the shredded chicken to the soup along with the chopped broccoli florets and baby spinach. Simmer for another 5 minutes until the greens are just wilted and the broccoli is tender-crisp.
Stir in the basil pesto and lemon juice. Taste and adjust seasoning if necessary. Add the egg noodles, cooking according to package instructions (usually 6-8 minutes) until al dente.
Once the noodles are cooked, remove the soup from heat. Stir in the chopped parsley. Serve hot, topped with freshly grated Parmesan and a sprinkle of fresh dill if desired.