Remove fully thawed chicken breasts from the refrigerator and bring to room temperature, about 20 minutes. Pat dry on all sides with paper towels.

Season chicken breasts with salt, pepper, dried thyme, and garlic powder.

In a large cast-iron pan, add 2 tablespoons olive oil and bring to medium-high heat.

Sear chicken in pan until lightly golden brown, then flip and sear again, about 3 minutes on each side.

Remove chicken from pan and place on a plate. Add remaining 1 tablespoon olive oil to pan and sear boiled potato wedges and green beans on both sides until browned, about 1 1/2 to 2 minutes. Season with a pinch of salt and pepper.

Remove potatoes and green beans from pan and set aside. Add butter, shallots, and garlic to pan and sauté for 20 to 30 seconds, or until fragrant and tender.

Add chicken stock and wine to pan, bring to a boil, and reduce by 1/3 in volume, about 3 minutes.

Add heavy cream to pan, bring to a boil, then add chicken breasts back into the pan. Reduce to a medium simmer, continuously basting the chicken with sauce and reducing until it thickens, about 4 to 5 minutes.

Once sauce has thickened, add potatoes and green beans, and baste vegetables until heated throughout and fully coated in sauce. Season to taste with additional salt and pepper, if needed.

Garnish with chopped parsley. Serve creamy chicken skillet family-style in the cast-iron pan.