In a large mixing bowl, cream shortening and sugar. Add egg; beat well. Add bananas and vanilla; mix well.
Combine the flour, baking soda and salt; stir into creamed mixture.
Fill prepared muffin cups three-fourths full. Bake for 23-28 minutes or until a toothpick inserted in muffin comes out clean.
Cool for 5 minutes before removing from pan to a wire rack to cool completely.
For Caramel Icing, in a small saucepan, melt butter over medium heat. Stir in brown sugar, salt and milk; bring to a boil. Cool slightly. Whisk in vanilla and powdered sugar. Transfer to a small resealable plastic bag; cut a small hole in a corner of bag and drizzle over muffins.