Preheat oven to 350 degrees and prepare loaf pan.
In medium bowl, combine all flour but 2 Tbsp, baking powder, baking soda, salt, and pudding mix. Whisk to combine and set aside.
In small bowl, combine remaining flour and chocolate chips, tossing well to combine and set aside.
In bowl of stand mixer, combine shortening and sugar. Beat on high until light and fluffy, about 2 minutes.
Add eggs, one at a time until thoroughly combined. Add milk and vanilla, then banana mixture, and combine well.
With mixer on low, add flour mixture until just combined then fold in chocolate chips.
Spread into loaf pan, tap to remove air pockets, and place in oven to bake. Bake loaf in oven for 1hr or until toothpick inserted into center comes out clean. Let loaf cool in pan for 5 minutes, then turn out onto wire rack to cool completely