Position a rack in the middle of the oven and heat to 350.
In a small bowl, mix the sugar with the chopped walnuts.
Generously butter a large bundt pan and coat with the nuts and sugar, pressing the nuts with your fingers to help them stick. The pan sides will be coated and some of the nuts will fall to the bottom, that’s fine.
In a medium bowl, whisk the flour, baking powder, baking soda and salt until well blended.
With an electric mixer, beat the butter, sugar, bananas and vanilla until well blended and the bananas are almost smooth, scraping down the sides of the bowl as needed.
Add the eggs one at a time, beating until just incorporated.
Remove the bowl from the mixer. With a rubber spatula alternately add half the flour mixture, all the buttermilk and the rest of the flour mixture, stirring until each addition is just blended.
Spoon half the batter into a medium bowl and gently stir in the melted chocolate until just combined.
With a large spoon, alternately add a scoopful of each batter to the prepared pan, working around the pan until all the batter is used.
Gently run a knife or the tip of a rubber spatula through the batter, once clockwise and once counterclockwise, to slightly swirl the batters.
Gently tap the pan on the counters to settle the ingredients.
Bake the cake until a pick inserted in the batter comes out with just a few crumbs sticking to it, about 40 minutes.
Let the cake cool in the pan on a wire rack for 15 minutes*.
Gently tap the sides of the pan on the counter to loosen the cake.
Invert the pan onto a rack, lift off the pan and let the cake cool completely.
*Be sure to follow the time guidelines for unmolding the cake. If you wait too long, it will stick to the pan; take it out too early and it might break into chunks.