Lightly grease twelve 2-1/2-inch muffin cups or line with paper bake cups; set aside.
In a large bowl combine flour, brown sugar, baking powder, baking soda, apple pie spice, and salt. Make a well in center of flour mixture; set aside.
In another bowl mash the drained sweet potatoes with a fork. Stir in egg, milk, jam, and oil. Add sweet potato mixture all at once to flour mixture. Stir just until moistened (batter should be lumpy).
Spoon batter into prepared muffin cups, filling each about three-fourths full. Bake in a 400 degree F oven for 18 to 20 minutes or until golden and a wooden toothpick inserted in centers comes out clean. Cool in muffin cups on a wire rack for 5 minutes. Remove from muffin cups. Cool slightly. Drizzle muffins with Jam Icing and, if desired, top with additional jam or preserves. Makes 12 muffins.
In a small bowl stir together powdered sugar, fruit jam or preserves, vanilla, and enough milk (2 to 3 teaspoons) to make icing of drizzling consistency. Makes about 1/4 cup.