In a saute pan over medium heat, add 1 tablespoon of the oil. When the oil is hot add the onions and saute until translucent. Stir in the artichokes and sun-dried tomatoes. Saute for 3 to 5 minutes, then add the salt, pepper and garlic. When the garlic begins to lightly brown, deglaze with 1/4 cup of the white wine. Stir in 2 tablespoons of the butter, allow it to melt, then toss in the Parmesan and parsley.
Remove from the heat and allow to cool before stuffing the chicken breast.
Rinse, trim and pound out chicken breasts to about 1/4-inch thick. Do not over-pound as holes in the chicken will make it difficult for the chicken to retain the stuffing.
Put 1/4 of the stuffing mixture at 1 end of a chicken breast. Gentle roll the chicken breast folding the ends in to help keep the stuffing from coming out during the cooking process. Secure the chicken roll with 2 toothpicks. Repeat with remaining chicken breasts and stuffing.
Heat the 2 tablespoons of the remaining oil in a medium saute pan over high heat. Add the chicken breasts, with the secured side of the chicken first, to insure the roll with stay together. Brown the chicken on all sides, add remaining butter, and deglaze with remaining white wine.
Reduce the heat to low and cover the pan. Cook until the internal temperature reaches 165 degrees F on an instant-read thermometer, about 10 minutes.
Remove the chicken to a cutting board and discard the toothpicks. Slice each breast on a bias into 5 pieces and transfer to a serving platter. Drizzle with remaining pan drippings, garnish with a sprinkle of Parmesan and serve.