In a large Dutch oven or heavy-bottomed pot, heat the butter and olive oil over medium heat. Add the leeks, onion, carrot, and celery. Cook, stirring occasionally, until the vegetables are softened, about 5 to 7 minutes. Stir in the minced garlic, salt, black pepper, and crushed red pepper flakes. Cook for another 1 to 2 minutes, until fragrant.
Using kitchen twine, tie the thyme and rosemary sprigs together into a small bouquet. This makes it easier to remove later.
Pour in the bone broth and add the parmesan rind. Nestle the chicken breasts into the broth. Add the herb bouquet. Bring the soup to a gentle simmer, cover, and cook for 20 to 25 minutes, or until the chicken is cooked through and tender.
Remove the chicken breasts and transfer them to a cutting board. Use two forks to shred the chicken into bite-sized pieces, then return it to the pot. Discard the herb bouquet and parmesan rind.
Stir in the lemon juice, chopped kale, and frozen peas. Simmer for another 3 to 5 minutes, until the kale is tender and the peas are warmed through. Stir in the fresh dill.
Meanwhile, bring a large pot of salted water to a boil. Cook the egg noodles according to the package instructions until al dente. Drain and set aside.
To serve, place a portion of cooked noodles in each bowl and ladle the hot soup over the top. Top with freshly grated parmesan and some fresh dill and serve!
