Heat the oil in a Dutch Oven over Medium-high heat. Add the Onion, Carrots, Celery, Garlic, Salt and Black Pepper. Cook until just tender. About 15 minutes
Add the Chicken Stock and Potatoes. Bring to a boil then turn the heat down to medium. Allow to simmer for about 15 more minutes
In a bowl combine the Butter and Flour. Use a fork to mash into a paste
Stir that paste by tablespoon amounts into the Stew. Turn the heat to low and allow to continue simmering for 5 more mintes
Using the same bowl you made the paste in add the Egg Yolks and Heavy Cream. Whisk them together. Slowly pour about a 1/4 C of the broth into the Egg mixture to temper it then stir that mixture into the Stew.
Add the shredded Chicken, Peas and Corn. Allow to cook for another minute. Serve with a slice of buttered Toast