Sprinkle chicken with 1 /8 teaspoon each salt and pepper. Heat sun-dried tomato oil in a large skillet over medium heat. Add the chicken and cook, turning once until browned, about 6 minutes total. Transfer to a plate.
Add sun-dried tomatoes and shallots to the pan. Cook, stirring, for 1 minute. Increase heat to high and add wine. Cook, scraping up any browned bits, until the liquid has mostly evaporated, about 2 minutes.
Reduce heat to medium and stir in cream, any accumulated juices from the chicken and the remaining 1 /8 teaspoon each salt and pepper; simmer for 2 minutes.
Return the chicken to the pan and turn to coat with the sauce. Serve the chicken topped with the sauce and parsley.
*Please use safe handling and cooking procedures when preparing any food.