Scrub potatoes and cut each in half. With a melon-baller or a spoon, scoop out a well in each potato half, leaving a shell 1/4 to 1/2 inch thick. Reserve scooped-out potato for other uses.
Lightly oil a 10- by 15-inch pan. Arrange potatoes in a single layer, cut sides up, in pan. Brush lightly with 1 tablespoon olive oil total.
Bake in a 400° oven for 20 minutes, then turn potatoes over and bake until cut sides are lightly browned, 5 to 10 minutes longer.
Meanwhile, heat mincemeat in a microwave-safe bowl in a microwave oven at full power (100%) until hot, about 1 minute, stirring once.
Spoon mincemeat equally into potatoes. Sprinkle with parsley. Serve hot, warm, or at room temperature.