Add 2 tablespoon of vegetable oil to a saute pan over low-medium heat.
When the oil begins to sizzle, add the chicken breasts and brown on each side, for a total of about 10 minutes. Then, remove the chicken and set aside.
In the same pan, saute onion, celery, and carrots for about 5 minutes, until they begin to soften.
Add garlic and saute for 30 seconds.
At this point, add butter and flour to the pan, whisk it together quickly, and then add the stock.
Add the bay leaves, thyme, parsley, peas, and cream. Add the chicken back to the pan. Simmer for 30 minutes.Taste the sauce and add salt and pepper as needed.
After 30 minutes, remove the chicken and using two forks, shred the chicken into bite-size pieces. Add the shredded chicken back to the pan.