Special equipment: a 6-mini Bundt pan
For the cakes: Cover the dates with boiling water and allow to rehydrate for 10 minutes, then drain and mash with the banana until smooth. Whisk in the melted butter, brown sugar, brandy, vanilla, salt and egg. Sift in the flour, baking powder and baking soda and stir until just combined.
Coat a 6-mini Bundt pan well with cooking spray, then coat with a 50/50 mixture of flour and granulated sugar. Tap the excess out, and divide the batter evenly among the cavities. Place in the refrigerator for 15 minutes. In the meantime, preheat the oven to 350 degrees F.
Line a baking sheet with aluminum foil, then place a wire cookie or roasting rack on top. Bake the cakes until they spring back when lightly touched, approximately 20 minutes. Place the pan on the prepared rack to cool for 5 minutes, then flip the pan upside down on the rack and let sit an additional 5 minutes. Gently lift the pan to release the cakes, then cool completely, about 30 minutes.
For the glaze: In a small saucepan, cook the evaporated milk and brown sugar together, stirring occasionally, until it becomes a thick caramel, about 10 minutes.
In a separate bowl, sift together the powdered sugar and salt, then whisk in the brandy. Add some ice water a teaspoon at a time until you have a glaze the consistency of maple syrup.
Whisk the butter and glaze into the caramel until smooth, and allow to rest to thicken slightly, 10 minutes. Carefully dip the tops of the Bundt cakes halfway into the caramel, then place them back on the wire rack so that the glaze can drip down and coat them completely. Allow the glaze to harden, about 15 minutes.