Arrange rack in upper third of oven. Preheat broiler to high. Line a baking sheet with foil.
Place salmon on the prepared baking sheet, skin-side down. Sprinkle with ¼ teaspoon each salt and pepper. Broil, rotating the pan from front to back once, until the salmon is opaque in the center, 8 to 12 minutes. Cut into 4 portions.
Meanwhile, heat sun-dried tomato oil in a large skillet over medium heat. Add sun-dried tomatoes and shallots; cook, stirring, for 1 minute. Increase heat to high and add wine and broth. Cook until the liquid has mostly evaporated, about 2 minutes. Reduce heat to medium and stir in cream and the remaining ¼ teaspoon each salt and pepper; simmer for 2 minutes. Serve the salmon topped with the sauce and parsley and with the rice on the side.