Chicken:

1. Preheat oven to 425F. Line a small baking dish with parchment paper for easy cleanup and set aside.
2. Pat dry the chicken breast with a couple of sheets of paper towel to remove excess moisture. Rub chicken all over with olive oil. 
3. Mix salt, pepper, garlic powder, and rosemary in a bowl and sprinkle all over the chicken. 
4. Bake chicken skin side up for 20-25 minutes on the middle rack or until thickest part reaches 165F. Remove from the oven and let rest until cool enough to handle. Discard the skin and bones. Shred or chop into bite-size pieces and toss with all pan juices before adding to the soup.

Soup:

1. Melt the butter in a large pot over medium-high heat. Add the onion, carrots, and celery with a pinch of salt. Cook, stirring occasionally, until softened and lightly golden, about 7-8 minutes. Add the garlic, thyme, and oregano and cook for 1 minute until fragrant.
2. Pour in the chicken stock. Add the bay leaf, salt, and black pepper. Bring the mixture to a gentle boil. Lower the heat and let the soup simmer for 20 minutes, partially covered. Taste and adjust seasoning as needed.
3. Increase the heat slightly to bring the soup back to a low boil. Add the egg noodles and cook, partially covered, according to package instructions until just tender, stirring occasionally to prevent sticking. Stir in the cooked chicken in the last 3-5 minutes of cooking. 
4. Remove the bay leaf. Stir in lemon juice just before serving to brighten the broth. Taste for salt and pepper, and add more if needed. Serve garnished with dill or parsley.