Preheat the oven to 350 °F (175 °C) (or 325 °F (165 °C) if using a dark loaf pan). Grease, flour, and line the bottom of a medium (8x4") loaf pan. I like the pan from Baker's Secret (available from Amazon).
Sift together the flours, salt, and baking powder into a medium bowl, then whisk in the freshly ground cardamom.
In the bowl of an electric mixer fitted with the paddle attachment, beat together the butter and the sugar for 3 minutes then, with the mixer on low, gradually add the whisked egg, a little at a time, then the vanilla. Scrape down the bowl and beat for another 3 minutes.
In a small bowl, combine the banana chunks with 2 scoops of the dry mixture, and stir to coat the fruit.
With the mixer on low, add a third of the flour and mix until almost combined, followed by half the buttermilk. Mix until just combined. Add another third of flour, and then the last of the buttermilk. Take the bowl off the mixer and then add the last bit of flour, mixing it in with a spatula by hand. Before the last of the flour has disappeared, stir in the flour-coated banana chunks.
Transfer the cake batter to the prepared pan, smoothing the top and tapping the pan on the counter several times to try and remove air pockets.
Bake for about 80 minutes or until a cake tester comes out clean.
Let cool 15 minutes before unmolding on a wire rack to cool completely.
Milk glaze
In a small bowl or a measuring cup with a pouring spout, whisk together the icing sugar with the milk. Adjust the consistency with more milk or powdered sugar. It should be thick but pourable.
Set the wire rack with the cake over a big sheet pan, then pour the glaze over the cake.