Warm oil in large pot over medium heat and add onions, carrots, and celery.
Cook until the vegetables are tender, about six minutes.
Add broth, thyme, and potatoes, cover and bring to a gentle simmer over high heat. Simmer until the potatoes are cooked, about 15 minutes, and then add the cooked chicken, peas, salt and pepper.
Stir flour and butter together in a small saucepan and stir together to form a smooth paste.
Gradually stir the paste into the stew and simmer over low heat until the stew thickens, 3-4 minutes.
Mix together the egg yolks and the kefir. Add 1/4 cup hot stew to the mix and then whisk the egg mixture back into the stew. Cook on low for one more minute.
Garnish with parsley and enjoy!