
Rinse the potatoes and transfer them to a large saucepan. Cover them with cold water by at least 3 inches.
Season with a generous amount of salt and bring it to a boil over high heat. Once the water reaches a rolling boil, reduce heat to medium and simmer the potatoes until tender (12-15 minutes).
Drain the potatoes and transfer them to a large mixing bowl.
Use a potato masher or a hand mixer to combine the boiled potatoes with the milk, butter, sour cream, salt, and pepper until nice and creamy. Set aside.
Heat the oil in a large cast-iron skillet over medium-high. Cook the shredded chicken for about 2 minutes.
Add the thyme, bay leaf, carrot, celery, onions, and garlic to the skillet. Stir well and cook for 4-6 minutes or until the vegetables soften.
Lower the heat to medium, add the white wine, and simmer on low until most of the liquid has evaporated.
Add flour, Worcestershire sauce, chicken broth, and optional chicken bouillon.
Simmer the mixture on low. Stir occasionally until the sauce thickens slightly (10-15 minutes).
Add peas and corn, stir well, and heat through. Season with salt and pepper, and set aside.
Preheat oven to 425°F/218℃. Spray a 9x13 casserole dish generously with nonstick coating.
Add the chicken filling. Spread the mashed potatoes evenly using a spatula until the filling is covered.
Transfer the shepherd's pie to the oven and bake until the potatoes brown slightly around the edges (18-20 minutes).
Let it rest for about 10 minutes before serving. Garnish with chopped parsley if desired.