Preheat oven to 350° F. Grease muffin pans.
Combine apple juice, 1/2 cup brown sugar and cinnamon in a small saucepan. Bring to a boil. Add crackers and reduce heat to medium. Cook until mixture is about the consistency of applesauce. Remove from heat and stir in raisins.
Combine flour, baking soda, salt, butter, egg and remaining 1/2 cup brown sugar in a large bowl. Beat until smooth. Stir in cracker mixture.
Fill muffin cups 2/3 full. Bake for 18 to 20 minutes or until tester inserted in center of muffins comes out clean. Remove from pan and place on wire rack to cool.
Combine all glaze ingredients until smooth. Drizzle over cooled muffinsServings: 12 muffins