Combine apples, brown sugar, raisins, water and 1 tablespoon rum in heavy medium saucepan. Cover and cook over medium heat until apples are tender, stirring until occasionally, about 15 minutes. Cool apple mixture completely. Preheat oven to 400°F. Roll out pastry to 10-inch square. Cut out four 4 1/2-inch pastry rounds, using 1-pound coffee can or individual tart pan bottom as guide (reserve remaining pastry for another use). Press 1 tablespoon pecans in center of each round, leaving border. Transfer rounds to baking sheet. Spoon 1/4 of apple mixture onto each round, leaving 1/2-inch border. Bake tartlets until brown on bottom and puffed at edges, about 20 minutes. Let cool 15 minutes. Beat cream, powdered sugar and remaining 1 tablespoon rum in medium bowl until stiff peaks form. Serve tartlets with rum cream.