In a large pot, heat butter and olive oil over medium heat.
Add the carrots, celery, onion, and garlic. Sauté for about 5 minutes, until the veggies begin to soften.
Pour in the chicken broth and add the chicken. Bring to a boil, then reduce heat and simmer until the chicken is fully cooked.
Remove the chicken from the pan, shred it, and return it to the soup along with the egg noodles.
Continue simmering until the noodles are tender.
Stir in the lemon juice and chopped rosemary. Reduce heat to low.
Slowly add in the heavy cream while stirring, and season with salt and pepper to taste.
Serve warm and enjoy.
