Preheat oven to 350°F. In a large bowl, combine flour, baking soda and salt. Set aside.
With a hand mixer or stand mixer fitted with a paddle attachment, beat butter until smooth and creamy. Add sugar and beat for another minute, at medium speed, scraping down the bowl as necessary. Add vanilla, then beat in 1 egg at a time. Mix in bananas (the mixture might curdle, that's ok).
Add half of the dry ingredients, sour cream, and then the remaining dry ingredients, mixing between each addition.
Thoroughly grease a 12-cup bundt pan and add the batter to the pan. Rap the pan on the counter a couple times (to remove air bubbles), then smooth out the top. Bake for 55-65 minutes, until a toothpick inserted into the center comes out clean. Loosely cover the cake with foil if it starts to get dark (this was around 30 minutes for me). Place the pan on a wire rack until it is cool enough to handle, then carefully unmold the cake and place it back on the rack to cool completely.
In a small saucepan combine butter, brown sugar and milk. Bring to a simmer, whisking frequently and cook until the sugar is dissolved, a minute or two. Remove from the heat and cool for 5 minutes.
Add vanilla, whisking to combine. Add powdered sugar ¼ cup at a time, whisking vigorously, until you reach your desired consistency. The icing will start to firm up quickly so have the cake cooled and ready. Drizzle the icing over the cake and immediately sprinkle with nuts. The icing will set in a matter of minutes.