Preheat the oven to 325°F.

Mix together the flour, baking powder, baking soda, and salt in a bowl.

In a separate bowl, cream together the softened butter and shortening.

Gradually beat in the light brown sugar and white sugar, mixing constantly for 5 to 7 minutes until light and fluffy.

Add the eggs one at a time, beating well after each addition until the yellow disappears.

Alternately add the flour mixture and milk to the butter mixture, beginning and ending with the flour mixture. Beat at low speed until just blended after each addition.

Stir in the mashed banana, chopped pecans, and vanilla extract.

Pour the batter into a greased and floured 10-inch tube pan.

Bake for 65 minutes, or until a wooden pick inserted into the center comes out clean.

Cool the cake on a wire rack for 10 minutes before removing it from the pan.

Cool completely on a wire rack.

To make the caramel glaze, combine the butter, brown sugar, white sugar, and whipping cream in a heavy saucepan over high heat.

Stir frequently and bring the mixture to a boil.

Boil for 1 minute without stirring.

Remove the saucepan from the heat.

Stir in the vanilla extract.

Cool the glaze until slightly thickened.

Drizzle the glaze over the cooled cake.