Put large stock pot with a lid over a high flame and heat the oil.
Add the carrots onions and celery and cook for 5 minutes. Add in the sausage and cook while breaking it apart with a wooden spoon until browned, about 5 minutes.
Add in the tomatoes and cook until they just begin to break down, about 5 minutes.
Add in the water and the bullion vibes. Cover the pot and bring to a boil.
Once boiling add in the Escarole and cook until tender, about 10 minutes. Taste for seasoning and season with salt as desired.
Lower the flame to a simmer.
In a small bowl whisk together the eggs and grated cheese. Stream the mixture into the broth while stirring with a wooden spoon.
Serve with an extra sprinkle of grated cheese and crusty Italian bread.