Sprinkle salt and pepper on both sides of the raw chicken breast.
Heat the oil in a large pot or Dutch oven over medium-high heat. Add the chicken and cook for 3-4 minutes on each side.
Remove the chicken and add the butter to the pot. Once melted, add the onion, celery, and carrot. Reduce heat to medium and cook for 5 minutes, stirring occasionally.
Add the garlic and cook for another minute.
Stir in the flour and cook until the juices in the pot have thickened.
Add the chicken, chicken broth, Italian seasoning, and a pinch of salt and pepper to the pot. Stir until well combined.
Bring to a simmer over medium heat, then cover and reduce the heat to medium-low. Allow to simmer for 18-20 minutes, stirring occasionally to ensure the soup is still simmering.
Remove the chicken from the soup and shred it.
Add the milk and heavy cream to the pot and stir. Bring the soup back to a simmer.
Add the noodles and cook uncovered until they are al dente, about 5-7 minutes. Once the noodles are cooked, return the shredded chicken to the pot.
Garnish with your favorite toppings, such as fresh parsley.
Notes
It’s best to store any leftover soup in an airtight container in the fridge, and then use leftovers within 3 to 4 days. You can freeze this soup but the vegetables and noodles might change texture once they’re thawed and reheated.