Mix the flour, baking powder, baking soda and salt together.
Cream the butter and shortening together, then beat in the brown and white sugars gradually, beating constantly for 5 to 7 minutes. Add the eggs one at a time, beating until the hellow dissappears.
Add the flour mixture alternately with the milk, beating at low speed until blended after each addition, beginning and ending with the flour mixture.
Stir in the banana, pecans and vanilla. Pour into a greased and floured 10 inch tube pan.
Bake for 65 minutes or until a woodenpick inserted in the center comes out clean. Cool on a wire rack for 10 minutes before removing from the pan to cool completely on a wire rack.
To make the glaze, bring the butter, brown sugar, white sugar and cream to a boil in a heavy saucepan over high heat, stirring frequently. Boil for 1 minute, without stirring. Remove from the heat. Stir in the Vanilla. Cool until slightly thickened, then drizzle over the cooled cake.