Preheat the oven to 350°F. Spread the walnuts in a single layer on a baking sheet pan. Toast for 6-8 minutes, then cool completely.
Use a whisk to sift together the all purpose flour, cake flour, banana pudding mix, baking powder, baking soda and salt. Set aside.
In the bowl of a stand mixer cream together the softened butter, sugar and vanilla until pale yellow and fluffy. Around 3 minutes on medium-high speed
Add the eggs one at a time beating well after each addition. Stop peridically and scrape the sides of the bowl as needed.
To the bowl add the sifted dry ingredients to the creamed mixture alternately with the buttermilk.
After all of the ingredients have been added increase the mixer speed and beat for 30-60 seconds or just until fully combined. Stop to scrape the side of the bowl and the beater as needed.
By hand, mix in 1 1/4 cup milk chocolate chips, 1 1/2 cup toasted walnuts and cubed banana into the batter.
Spray a standard 12-14 cup bundt pan with baking spray. Pour the cake batter evenly into the pan. The batter will be thick.
Bake for 45-55 minutes, or until a cake tester or toothpick inserted into the center comes back clean.
Check halfway through baking and cover the top with a piece of aluminum foil to prevent over-browning, if needed.
Cool in the pan for 10-15 minutes, then invert onto a wire rack to cool completely.
Milk Chocolate Glaze: Melt together 3/4 cup chocolate chips with heavy cream in a microwave safe bowl. Heat in 20 second increments (or using the melt function) stopping to stir each time. Repeat process until completely smooth.
Drizzle chocolate glaze over cooled cake and sprinkle the top with reserved toasted walnuts.