Heat the oil in a large Dutch oven over medium-high heat until shimmering.
Add the onion, carrot, and celery and cook until softened, 3-4 minutes.
Stir in the thyme, bone broth, and chicken.
Bring to a simmer and cook until the vegetables are tender, about 15 minutes.
Stir in parsley.
Stir soup gently so that it is moving in a circle.
Pour beaten eggs into soup in a slow steady stream. This will create “noodles” for the soup.
Remove soup from heat and let stand for 2 minutes.
Break up the eggs using a fork.
Season with sea salt and pepper to taste before serving.
