In a very small saucepan heat rosemary and vinegar over low heat until hot, but not boiling. Remove pan from heat and cover. Let stand for 20 minutes so that the vinegar becomes infused with the rosemary.
In a metal measuring cup heat oil over low heat or microwave until warm. (Heating thins oil, making it easier to brush sparingly over onions.) If you are using an indoor grill, place slices on the grill. For an outdoor grill, use a grilling basket to keep onion slices from falling through. If you don't have a basket, place a soaked bamboo skewer through the rings parallel to the cuts so that they do not tumble through the grill. Brush both sides of each slice lightly with oil. Season onions with salt and pepper and grill 4 to 6 minutes on each side, or until lightly charred and softened.
Transfer onions as grilled to a large bowl, separating rings, and toss with vinegar mixture, parsley, and salt and pepper to taste.